LMFDB - Embedded newform 390.2.bh.c.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(11,390)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("390.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bh (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	390.11
Dual form			390.2.bh.c.71.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-1.39472 - 1.02701i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.08139 + 1.35299i) q^{6} +(-0.213554 - 0.796995i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.890511 + 2.86478i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.39472 - 1.02701i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.08139 + 1.35299i) q^{6} +(-0.213554 - 0.796995i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.890511 + 2.86478i) q^{9} +(0.866025 - 0.500000i) q^{10} +(-0.981698 + 3.66375i) q^{11} +(-0.694363 - 1.58678i) q^{12} +(3.42697 - 1.12067i) q^{13} +0.825110i q^{14} +(1.71242 - 0.260015i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.49980 - 2.59772i) q^{17} +(-0.118707 - 2.99765i) q^{18} +(1.17350 - 0.314438i) q^{19} +(-0.965926 + 0.258819i) q^{20} +(-0.520671 + 1.33091i) q^{21} +(1.89649 - 3.28482i) q^{22} +(1.76190 + 3.05169i) q^{23} +(0.260015 + 1.71242i) q^{24} -1.00000i q^{25} +(-3.60025 + 0.195522i) q^{26} +(1.70014 - 4.91015i) q^{27} +(0.213554 - 0.796995i) q^{28} +(6.48200 - 3.74239i) q^{29} +(-1.72137 - 0.192053i) q^{30} +(0.00278407 + 0.00278407i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(5.13189 - 4.10170i) q^{33} +(-2.12103 + 2.12103i) q^{34} +(0.714566 + 0.412555i) q^{35} +(-0.661187 + 2.92623i) q^{36} +(10.9895 + 2.94462i) q^{37} -1.21489 q^{38} +(-5.93061 - 1.95649i) q^{39} +1.00000 q^{40} +(4.61510 + 1.23661i) q^{41} +(0.847394 - 1.15080i) q^{42} +(3.40698 + 1.96702i) q^{43} +(-2.68205 + 2.68205i) q^{44} +(-2.65539 - 1.39602i) q^{45} +(-0.912024 - 3.40372i) q^{46} +(-7.01463 - 7.01463i) q^{47} +(0.192053 - 1.72137i) q^{48} +(5.47258 - 3.15960i) q^{49} +(-0.258819 + 0.965926i) q^{50} +(-4.75968 + 2.08280i) q^{51} +(3.52818 + 0.742952i) q^{52} -4.90674i q^{53} +(-2.91305 + 4.30281i) q^{54} +(-1.89649 - 3.28482i) q^{55} +(-0.412555 + 0.714566i) q^{56} +(-1.95964 - 0.766637i) q^{57} +(-7.22973 + 1.93720i) q^{58} +(4.67330 - 1.25221i) q^{59} +(1.61301 + 0.631032i) q^{60} +(-6.87481 + 11.9075i) q^{61} +(-0.00196864 - 0.00340978i) q^{62} +(2.09305 - 1.32152i) q^{63} +1.00000i q^{64} +(-1.63080 + 3.21567i) q^{65} +(-6.01863 + 2.63371i) q^{66} +(-3.00389 + 11.2107i) q^{67} +(2.59772 - 1.49980i) q^{68} +(0.676753 - 6.06575i) q^{69} +(-0.583441 - 0.583441i) q^{70} +(1.52747 + 5.70060i) q^{71} +(1.39602 - 2.65539i) q^{72} +(-8.49044 + 8.49044i) q^{73} +(-9.85289 - 5.68857i) q^{74} +(-1.02701 + 1.39472i) q^{75} +(1.17350 + 0.314438i) q^{76} +3.12963 q^{77} +(5.22215 + 3.42478i) q^{78} +5.90955 q^{79} +(-0.965926 - 0.258819i) q^{80} +(-7.41398 + 5.10224i) q^{81} +(-4.13778 - 2.38895i) q^{82} +(-5.36244 + 5.36244i) q^{83} +(-1.11637 + 0.892267i) q^{84} +(0.776351 + 2.89738i) q^{85} +(-2.78179 - 2.78179i) q^{86} +(-12.8841 - 1.43747i) q^{87} +(3.28482 - 1.89649i) q^{88} +(1.85846 - 6.93588i) q^{89} +(2.20360 + 2.03572i) q^{90} +(-1.62501 - 2.49195i) q^{91} +3.52379i q^{92} +(-0.00102375 - 0.00674227i) q^{93} +(4.96009 + 8.59113i) q^{94} +(-0.607447 + 1.05213i) q^{95} +(-0.631032 + 1.61301i) q^{96} +(-7.65690 + 2.05166i) q^{97} +(-6.10387 + 1.63553i) q^{98} +(-11.3701 + 0.450254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9}+O(q^{10}) $ 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9	$ 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9} + 8 q^{13} + 4 q^{15} + 20 q^{16} - 8 q^{18} - 16 q^{19} + 4 q^{21} - 8 q^{22} + 8 q^{24} - 48 q^{27} + 8 q^{28} + 36 q^{31} + 12 q^{33} + 16 q^{34} - 12 q^{36} - 64 q^{37} - 60 q^{39} + 40 q^{40} - 12 q^{42} + 8 q^{45} - 32 q^{46} + 48 q^{49} + 24 q^{52} - 28 q^{54} + 8 q^{55} - 76 q^{57} - 28 q^{58} + 4 q^{60} - 40 q^{61} + 80 q^{63} + 40 q^{66} - 28 q^{67} - 36 q^{69} + 16 q^{70} + 16 q^{72} + 8 q^{73} - 16 q^{76} - 28 q^{78} + 40 q^{79} + 12 q^{81} + 20 q^{84} + 44 q^{85} + 40 q^{87} + 12 q^{88} + 120 q^{91} - 8 q^{93} - 16 q^{94} + 4 q^{96} - 160 q^{97} - 96 q^{99}+O(q^{100}) $ 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9 + 8 * q^13 + 4 * q^15 + 20 * q^16 - 8 * q^18 - 16 * q^19 + 4 * q^21 - 8 * q^22 + 8 * q^24 - 48 * q^27 + 8 * q^28 + 36 * q^31 + 12 * q^33 + 16 * q^34 - 12 * q^36 - 64 * q^37 - 60 * q^39 + 40 * q^40 - 12 * q^42 + 8 * q^45 - 32 * q^46 + 48 * q^49 + 24 * q^52 - 28 * q^54 + 8 * q^55 - 76 * q^57 - 28 * q^58 + 4 * q^60 - 40 * q^61 + 80 * q^63 + 40 * q^66 - 28 * q^67 - 36 * q^69 + 16 * q^70 + 16 * q^72 + 8 * q^73 - 16 * q^76 - 28 * q^78 + 40 * q^79 + 12 * q^81 + 20 * q^84 + 44 * q^85 + 40 * q^87 + 12 * q^88 + 120 * q^91 - 8 * q^93 - 16 * q^94 + 4 * q^96 - 160 * q^97 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−1.39472	−	1.02701i	−0.805244	−	0.592943i
$3$	−1.39472	−	1.02701i	−0.805244	−	0.592943i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	1.08139	+	1.35299i	0.441476	+	0.552358i
$7$	−0.213554	−	0.796995i	−0.0807159	−	0.301236i	0.913753	−	0.406271i	$-0.133171\pi$
$7$	−0.213554	−	0.796995i	−0.0807159	−	0.301236i	−0.994469	+	0.105035i	$0.966504\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.890511	+	2.86478i	0.296837	+	0.954928i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$	−0.981698	+	3.66375i	−0.295993	+	1.10466i	0.644433	+	0.764661i	$0.277094\pi$
$11$	−0.981698	+	3.66375i	−0.295993	+	1.10466i	−0.940426	+	0.340000i	$0.889573\pi$
$12$	−0.694363	−	1.58678i	−0.200445	−	0.458063i
$13$	3.42697	−	1.12067i	0.950469	−	0.310819i
$13$	3.42697	−	1.12067i	0.950469	−	0.310819i
$14$			0.825110i			0.220520i
$15$	1.71242	−	0.260015i	0.442146	−	0.0671356i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.49980	−	2.59772i	0.363754	−	0.630040i	−0.624822	−	0.780768i	$-0.714828\pi$
$17$	1.49980	−	2.59772i	0.363754	−	0.630040i	0.988575	+	0.150727i	$0.0481616\pi$
$18$	−0.118707	−	2.99765i	−0.0279795	−	0.706553i
$19$	1.17350	−	0.314438i	0.269219	−	0.0721370i	−0.121684	−	0.992569i	$-0.538829\pi$
$19$	1.17350	−	0.314438i	0.269219	−	0.0721370i	0.390903	+	0.920432i	$0.372163\pi$
$20$	−0.965926	+	0.258819i	−0.215988	+	0.0578737i
$21$	−0.520671	+	1.33091i	−0.113620	+	0.290428i
$22$	1.89649	−	3.28482i	0.404334	−	0.700327i
$23$	1.76190	+	3.05169i	0.367381	+	0.636322i	0.989155	−	0.146874i	$-0.0469213\pi$
$23$	1.76190	+	3.05169i	0.367381	+	0.636322i	−0.621775	+	0.783196i	$0.713588\pi$
$24$	0.260015	+	1.71242i	0.0530753	+	0.349547i
$25$		−	1.00000i		−	0.200000i
$26$	−3.60025	+	0.195522i	−0.706066	+	0.0383451i
$27$	1.70014	−	4.91015i	0.327192	−	0.944958i
$28$	0.213554	−	0.796995i	0.0403580	−	0.150618i
$29$	6.48200	−	3.74239i	1.20368	−	0.694943i	0.242306	−	0.970200i	$-0.422096\pi$
$29$	6.48200	−	3.74239i	1.20368	−	0.694943i	0.961371	+	0.275256i	$0.0887627\pi$
$30$	−1.72137	−	0.192053i	−0.314278	−	0.0350638i
$31$	0.00278407	+	0.00278407i	0.000500034	+	0.000500034i	0.707357	−	0.706857i	$-0.249887\pi$
$31$	0.00278407	+	0.00278407i	0.000500034	+	0.000500034i	−0.706857	+	0.707357i	$0.749887\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	5.13189	−	4.10170i	0.893348	−	0.714015i
$34$	−2.12103	+	2.12103i	−0.363754	+	0.363754i
$35$	0.714566	+	0.412555i	0.120784	+	0.0697345i
$36$	−0.661187	+	2.92623i	−0.110198	+	0.487705i
$37$	10.9895	+	2.94462i	1.80666	+	0.484093i	0.994985	−	0.100020i	$-0.0318906\pi$
$37$	10.9895	+	2.94462i	1.80666	+	0.484093i	0.811673	+	0.584112i	$0.198557\pi$
$38$	−1.21489			−0.197082
$39$	−5.93061	−	1.95649i	−0.949658	−	0.313289i
$40$	1.00000			0.158114
$41$	4.61510	+	1.23661i	0.720757	+	0.193126i	0.600509	−	0.799618i	$-0.294965\pi$
$41$	4.61510	+	1.23661i	0.720757	+	0.193126i	0.120247	+	0.992744i	$0.461631\pi$
$42$	0.847394	−	1.15080i	0.130756	−	0.177572i
$43$	3.40698	+	1.96702i	0.519560	+	0.299968i	0.736755	−	0.676160i	$-0.236357\pi$
$43$	3.40698	+	1.96702i	0.519560	+	0.299968i	−0.217195	+	0.976128i	$0.569691\pi$
$44$	−2.68205	+	2.68205i	−0.404334	+	0.404334i
$45$	−2.65539	−	1.39602i	−0.395843	−	0.208107i
$46$	−0.912024	−	3.40372i	−0.134471	−	0.501851i
$47$	−7.01463	−	7.01463i	−1.02319	−	1.02319i	−0.999725	−	0.0234640i	$-0.992530\pi$
$47$	−7.01463	−	7.01463i	−1.02319	−	1.02319i	−0.0234640	−	0.999725i	$-0.507470\pi$
$48$	0.192053	−	1.72137i	0.0277204	−	0.248458i
$49$	5.47258	−	3.15960i	0.781797	−	0.451371i
$50$	−0.258819	+	0.965926i	−0.0366025	+	0.136603i
$51$	−4.75968	+	2.08280i	−0.666489	+	0.291651i
$52$	3.52818	+	0.742952i	0.489270	+	0.103029i
$53$		−	4.90674i		−	0.673992i	−0.941506	−	0.336996i	$-0.890589\pi$
$53$		−	4.90674i		−	0.673992i	0.941506	−	0.336996i	$-0.109411\pi$
$54$	−2.91305	+	4.30281i	−0.396415	+	0.585538i
$55$	−1.89649	−	3.28482i	−0.255723	−	0.442926i
$56$	−0.412555	+	0.714566i	−0.0551300	+	0.0954880i
$57$	−1.95964	−	0.766637i	−0.259560	−	0.101544i
$58$	−7.22973	+	1.93720i	−0.949310	+	0.254367i
$59$	4.67330	−	1.25221i	0.608412	−	0.163024i	0.0585576	−	0.998284i	$-0.481350\pi$
$59$	4.67330	−	1.25221i	0.608412	−	0.163024i	0.549854	+	0.835261i	$0.314683\pi$
$60$	1.61301	+	0.631032i	0.208239	+	0.0814659i
$61$	−6.87481	+	11.9075i	−0.880230	+	1.52460i	−0.0291445	+	0.999575i	$0.509278\pi$
$61$	−6.87481	+	11.9075i	−0.880230	+	1.52460i	−0.851085	+	0.525027i	$0.824055\pi$
$62$	−0.00196864	−	0.00340978i	−0.000250017	−	0.000433042i
$63$	2.09305	−	1.32152i	0.263699	−	0.166496i
$64$			1.00000i			0.125000i
$65$	−1.63080	+	3.21567i	−0.202275	+	0.398854i
$66$	−6.01863	+	2.63371i	−0.740842	+	0.324187i
$67$	−3.00389	+	11.2107i	−0.366984	+	1.36960i	0.497727	+	0.867334i	$0.334168\pi$
$67$	−3.00389	+	11.2107i	−0.366984	+	1.36960i	−0.864711	+	0.502269i	$0.832499\pi$
$68$	2.59772	−	1.49980i	0.315020	−	0.181877i
$69$	0.676753	−	6.06575i	0.0814715	−	0.730230i
$70$	−0.583441	−	0.583441i	−0.0697345	−	0.0697345i
$71$	1.52747	+	5.70060i	0.181277	+	0.676537i	0.995397	+	0.0958392i	$0.0305535\pi$
$71$	1.52747	+	5.70060i	0.181277	+	0.676537i	−0.814119	+	0.580698i	$0.802780\pi$
$72$	1.39602	−	2.65539i	0.164523	−	0.312941i
$73$	−8.49044	+	8.49044i	−0.993730	+	0.993730i	−0.999980	−	0.00625000i	$-0.998011\pi$
$73$	−8.49044	+	8.49044i	−0.993730	+	0.993730i	0.00625000	+	0.999980i	$0.498011\pi$
$74$	−9.85289	−	5.68857i	−1.14538	−	0.661283i
$75$	−1.02701	+	1.39472i	−0.118589	+	0.161049i
$76$	1.17350	+	0.314438i	0.134609	+	0.0360685i
$77$	3.12963			0.356655
$78$	5.22215	+	3.42478i	0.591292	+	0.387780i
$79$	5.90955			0.664877			0.332438	−	0.943125i	$-0.392129\pi$
$79$	5.90955			0.664877			0.332438	+	0.943125i	$0.392129\pi$
$80$	−0.965926	−	0.258819i	−0.107994	−	0.0289368i
$81$	−7.41398	+	5.10224i	−0.823776	+	0.566916i
$82$	−4.13778	−	2.38895i	−0.456942	−	0.263815i
$83$	−5.36244	+	5.36244i	−0.588605	+	0.588605i	−0.937253	−	0.348649i	$-0.886641\pi$
$83$	−5.36244	+	5.36244i	−0.588605	+	0.588605i	0.348649	+	0.937253i	$0.386641\pi$
$84$	−1.11637	+	0.892267i	−0.121806	+	0.0973543i
$85$	0.776351	+	2.89738i	0.0842071	+	0.314265i
$86$	−2.78179	−	2.78179i	−0.299968	−	0.299968i
$87$	−12.8841	−	1.43747i	−1.38132	−	0.154113i
$88$	3.28482	−	1.89649i	0.350163	−	0.202167i
$89$	1.85846	−	6.93588i	0.196997	−	0.735202i	−0.794744	−	0.606945i	$-0.792395\pi$
$89$	1.85846	−	6.93588i	0.196997	−	0.735202i	0.991741	−	0.128257i	$-0.0409384\pi$
$90$	2.20360	+	2.03572i	0.232280	+	0.214584i
$91$	−1.62501	−	2.49195i	−0.170348	−	0.261227i
$92$			3.52379i			0.367381i
$93$	−0.00102375	−	0.00674227i	−0.000106158	−	0.000699141i
$94$	4.96009	+	8.59113i	0.511594	+	0.886107i
$95$	−0.607447	+	1.05213i	−0.0623228	+	0.107946i
$96$	−0.631032	+	1.61301i	−0.0644044	+	0.164627i
$97$	−7.65690	+	2.05166i	−0.777440	+	0.208314i	−0.625656	−	0.780099i	$-0.715169\pi$
$97$	−7.65690	+	2.05166i	−0.777440	+	0.208314i	−0.151784	+	0.988414i	$0.548502\pi$
$98$	−6.10387	+	1.63553i	−0.616584	+	0.165213i
$99$	−11.3701	+	0.450254i	−1.14273	+	0.0452522i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	7.69191	+	13.3228i	0.765374	+	1.32567i	0.940049	+	0.341041i	$0.110779\pi$
$101$	7.69191	+	13.3228i	0.765374	+	1.32567i	−0.174675	+	0.984626i	$0.555887\pi$
$102$	5.13657	−	0.779939i	0.508596	−	0.0772254i
$103$		−	16.3952i		−	1.61547i	−0.589548	−	0.807733i	$-0.700694\pi$
$103$		−	16.3952i		−	1.61547i	0.589548	−	0.807733i	$-0.299306\pi$
$104$	−3.21567	−	1.63080i	−0.315322	−	0.159913i
$105$	−0.572926	−	1.30927i	−0.0559118	−	0.127771i
$106$	−1.26996	+	4.73954i	−0.123349	+	0.460345i
$107$	−0.677545	+	0.391181i	−0.0655008	+	0.0378169i	−0.532393	−	0.846497i	$-0.678707\pi$
$107$	−0.677545	+	0.391181i	−0.0655008	+	0.0378169i	0.466892	+	0.884314i	$0.345374\pi$
$108$	3.92744	−	3.40224i	0.377918	−	0.327381i
$109$	−0.503685	−	0.503685i	−0.0482443	−	0.0482443i	0.682573	−	0.730817i	$-0.260861\pi$
$109$	−0.503685	−	0.503685i	−0.0482443	−	0.0482443i	−0.730817	+	0.682573i	$0.760861\pi$
$110$	0.981698	+	3.66375i	0.0936012	+	0.349324i
$111$	−12.3031	−	15.3932i	−1.16776	−	1.46106i
$112$	0.583441	−	0.583441i	0.0551300	−	0.0551300i
$113$	−5.41625	−	3.12708i	−0.509518	−	0.294170i	0.223117	−	0.974792i	$-0.428377\pi$
$113$	−5.41625	−	3.12708i	−0.509518	−	0.294170i	−0.732636	+	0.680621i	$0.761710\pi$
$114$	1.69444	+	1.24771i	0.158699	+	0.116858i
$115$	−3.40372	−	0.912024i	−0.317399	−	0.0850467i
$116$	7.48477			0.694943
$117$	6.26224	+	8.81955i	0.578944	+	0.815367i
$118$	−4.83816			−0.445389
$119$	−2.39066	−	0.640575i	−0.219151	−	0.0587215i
$120$	−1.39472	−	1.02701i	−0.127320	−	0.0937525i
$121$	−2.93302	−	1.69338i	−0.266638	−	0.153944i
$122$	9.72246	−	9.72246i	0.880230	−	0.880230i
$123$	−5.16678	−	6.46447i	−0.465873	−	0.582882i
$124$	0.00101904	+	0.00380311i	9.15126e−5	+	0.000341530i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−2.36376	+	0.734770i	−0.210581	+	0.0654585i
$127$	0.683797	−	0.394790i	0.0606771	−	0.0350320i	−0.469355	−	0.883010i	$-0.655513\pi$
$127$	0.683797	−	0.394790i	0.0606771	−	0.0350320i	0.530032	+	0.847978i	$0.322180\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−2.73165	−	6.24245i	−0.240509	−	0.549617i
$130$	2.40750	−	2.68401i	0.211152	−	0.235404i
$131$		−	0.615603i		−	0.0537854i	−0.999638	−	0.0268927i	$-0.991439\pi$
$131$		−	0.615603i		−	0.0537854i	0.999638	−	0.0268927i	$-0.00856125\pi$
$132$	6.49520	−	0.986234i	0.565335	−	0.0858406i
$133$	−0.501211	−	0.868123i	−0.0434605	−	0.0752758i
$134$	5.80308	−	10.0512i	0.501309	−	0.868293i
$135$	2.26982	+	4.67418i	0.195355	+	0.402289i
$136$	−2.89738	+	0.776351i	−0.248448	+	0.0665716i
$137$	10.3607	−	2.77613i	0.885172	−	0.237181i	0.212534	−	0.977154i	$-0.431828\pi$
$137$	10.3607	−	2.77613i	0.885172	−	0.237181i	0.672637	+	0.739973i	$0.265162\pi$
$138$	−2.22362	+	5.68391i	−0.189287	+	0.483846i
$139$	11.5899	−	20.0743i	0.983042	−	1.70268i	0.332711	−	0.943029i	$-0.392037\pi$
$139$	11.5899	−	20.0743i	0.983042	−	1.70268i	0.650331	−	0.759651i	$-0.274630\pi$
$140$	0.412555	+	0.714566i	0.0348673	+	0.0603919i
$141$	2.57940	+	16.9875i	0.217224	+	1.43061i
$142$		−	5.90170i		−	0.495259i
$143$	0.741614	+	13.6557i	0.0620168	+	1.14195i
$144$	−2.03572	+	2.20360i	−0.169643	+	0.183633i
$145$	−1.93720	+	7.22973i	−0.160876	+	0.600397i
$146$	10.3986	−	6.00365i	0.860596	−	0.496865i
$147$	−10.8777	−	1.21362i	−0.897175	−	0.100097i
$148$	8.04485	+	8.04485i	0.661283	+	0.661283i
$149$	1.19718	+	4.46795i	0.0980772	+	0.366029i	0.997468	−	0.0711164i	$-0.0226562\pi$
$149$	1.19718	+	4.46795i	0.0980772	+	0.366029i	−0.899391	+	0.437145i	$0.855990\pi$
$150$	1.35299	−	1.08139i	0.110472	−	0.0882952i
$151$	−5.26555	+	5.26555i	−0.428504	+	0.428504i	−0.888119	−	0.459614i	$-0.847988\pi$
$151$	−5.26555	+	5.26555i	−0.428504	+	0.428504i	0.459614	+	0.888119i	$0.347988\pi$
$152$	−1.05213	−	0.607447i	−0.0853390	−	0.0492705i
$153$	8.77750	+	1.98329i	0.709619	+	0.160340i
$154$	−3.02299	−	0.810009i	−0.243600	−	0.0652724i
$155$	−0.00393727			−0.000316249
$156$	−4.15781	−	4.65968i	−0.332892	−	0.373073i
$157$	4.36770			0.348580			0.174290	−	0.984694i	$-0.444237\pi$
$157$	4.36770			0.348580			0.174290	+	0.984694i	$0.444237\pi$
$158$	−5.70819	−	1.52950i	−0.454119	−	0.121681i
$159$	−5.03925	+	6.84354i	−0.399639	+	0.542728i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	2.05592	−	2.05592i	0.162030	−	0.162030i
$162$	8.48191	−	3.00951i	0.666402	−	0.236450i
$163$	1.31903	+	4.92267i	0.103314	+	0.385574i	0.998148	−	0.0608248i	$-0.0193731\pi$
$163$	1.31903	+	4.92267i	0.103314	+	0.385574i	−0.894834	+	0.446398i	$0.852706\pi$
$164$	3.37848	+	3.37848i	0.263815	+	0.263815i
$165$	−0.728453	+	6.52914i	−0.0567100	+	0.508293i
$166$	6.56762	−	3.79182i	0.509747	−	0.294302i
$167$	2.38628	−	8.90571i	0.184656	−	0.689144i	−0.810048	−	0.586363i	$-0.800559\pi$
$167$	2.38628	−	8.90571i	0.184656	−	0.689144i	0.994704	−	0.102781i	$-0.0327742\pi$
$168$	1.30927	−	0.572926i	0.101012	−	0.0442022i
$169$	10.4882	−	7.68101i	0.806784	−	0.590847i
$170$		−	2.99959i		−	0.230058i
$171$	1.94581	+	3.08181i	0.148800	+	0.235672i
$172$	1.96702	+	3.40698i	0.149984	+	0.259780i
$173$	−2.74926	+	4.76186i	−0.209023	+	0.362038i	−0.951407	−	0.307937i	$-0.900362\pi$
$173$	−2.74926	+	4.76186i	−0.209023	+	0.362038i	0.742384	+	0.669974i	$0.233695\pi$
$174$	12.0730	+	4.72313i	0.915252	+	0.358059i
$175$	−0.796995	+	0.213554i	−0.0602472	+	0.0161432i
$176$	−3.66375	+	0.981698i	−0.276165	+	0.0739982i
$177$	−7.80399	−	3.05303i	−0.586584	−	0.229480i
$178$	−3.59028	+	6.21854i	−0.269103	+	0.466100i
$179$	−2.40507	−	4.16571i	−0.179764	−	0.311360i	0.762036	−	0.647535i	$-0.224200\pi$
$179$	−2.40507	−	4.16571i	−0.179764	−	0.311360i	−0.941800	+	0.336175i	$0.890867\pi$
$180$	−1.60163	−	2.53669i	−0.119378	−	0.189074i
$181$		−	9.68726i		−	0.720048i	−0.932943	−	0.360024i	$-0.882768\pi$
$181$		−	9.68726i		−	0.720048i	0.932943	−	0.360024i	$-0.117232\pi$
$182$	0.924678	+	2.82762i	0.0685417	+	0.209597i
$183$	21.8176	−	9.54723i	1.61280	−	0.705752i
$184$	0.912024	−	3.40372i	0.0672353	−	0.250926i
$185$	−9.85289	+	5.68857i	−0.724399	+	0.418232i
$186$	−0.000756163		0.00677750i	−5.54446e−5		0.000496951i
$187$	8.04505	+	8.04505i	0.588312	+	0.588312i
$188$	−2.56753	−	9.58216i	−0.187257	−	0.698851i
$189$	−4.27643	−	0.306419i	−0.311065	−	0.0222887i
$190$	0.859060	−	0.859060i	0.0623228	−	0.0623228i
$191$	4.55237	+	2.62831i	0.329398	+	0.190178i	0.655574	−	0.755131i	$-0.272427\pi$
$191$	4.55237	+	2.62831i	0.329398	+	0.190178i	−0.326176	+	0.945309i	$0.605760\pi$
$192$	1.02701	−	1.39472i	0.0741179	−	0.100656i
$193$	−0.170227	−	0.0456122i	−0.0122532	−	0.00328324i	0.252687	−	0.967548i	$-0.418686\pi$
$193$	−0.170227	−	0.0456122i	−0.0122532	−	0.00328324i	−0.264940	+	0.964265i	$0.585352\pi$
$194$	7.92700			0.569126
$195$	5.57702	−	2.81013i	0.399379	−	0.201237i
$196$	6.31919			0.451371
$197$	7.06564	+	1.89323i	0.503406	+	0.134887i	0.501580	−	0.865111i	$-0.332752\pi$
$197$	7.06564	+	1.89323i	0.503406	+	0.134887i	0.00182570	+	0.999998i	$0.499419\pi$
$198$	11.0992	+	2.50787i	0.788783	+	0.178227i
$199$	−16.9120	−	9.76412i	−1.19886	−	0.692160i	−0.238556	−	0.971129i	$-0.576674\pi$
$199$	−16.9120	−	9.76412i	−1.19886	−	0.692160i	−0.960300	+	0.278969i	$0.910007\pi$
$200$	−0.707107	+	0.707107i	−0.0500000	+	0.0500000i
$201$	15.7031	−	12.5508i	1.10761	−	0.885264i
$202$	−3.98163	−	14.8596i	−0.280146	−	1.04552i
$203$	−4.36692	−	4.36692i	−0.306498	−	0.306498i
$204$	−5.16341	−	0.576079i	−0.361511	−	0.0403336i
$205$	−4.13778	+	2.38895i	−0.288995	+	0.166851i
$206$	−4.24339	+	15.8365i	−0.295651	+	1.10338i
$207$	−7.17345	+	7.76502i	−0.498589	+	0.539706i
$208$	2.68401	+	2.40750i	0.186103	+	0.166930i
$209$			4.60808i			0.318748i
$210$	0.214541	+	1.41294i	0.0148047	+	0.0975020i
$211$	−3.04589	−	5.27563i	−0.209688	−	0.363189i	0.741929	−	0.670479i	$-0.233911\pi$
$211$	−3.04589	−	5.27563i	−0.209688	−	0.363189i	−0.951616	+	0.307289i	$0.900578\pi$
$212$	2.45337	−	4.24936i	0.168498	−	0.291847i
$213$	3.72416	−	9.51949i	0.255175	−	0.652265i
$214$	0.755704	−	0.202490i	0.0516588	−	0.0138419i
$215$	−3.79999	+	1.01821i	−0.259157	+	0.0694410i
$216$	−4.67418	+	2.26982i	−0.318037	+	0.154442i
$217$	0.00162434	−	0.00281344i	0.000110267	−	0.000190989i
$218$	0.356159	+	0.616886i	0.0241221	+	0.0417808i
$219$	20.5616	−	3.12208i	1.38942	−	0.210970i
$220$		−	3.79299i		−	0.255723i
$221$	2.22855	−	10.5831i	0.149909	−	0.711895i
$222$	7.89986	+	18.0530i	0.530204	+	1.21164i
$223$	−2.15128	+	8.02867i	−0.144060	+	0.537640i	0.855735	+	0.517414i	$0.173105\pi$
$223$	−2.15128	+	8.02867i	−0.144060	+	0.537640i	−0.999795	+	0.0202258i	$0.993561\pi$
$224$	−0.714566	+	0.412555i	−0.0477440	+	0.0275650i
$225$	2.86478	−	0.890511i	0.190986	−	0.0593674i
$226$	4.42235	+	4.42235i	0.294170	+	0.294170i
$227$	5.28248	+	19.7145i	0.350611	+	1.30850i	0.885919	+	0.463840i	$0.153529\pi$
$227$	5.28248	+	19.7145i	0.350611	+	1.30850i	−0.535309	+	0.844657i	$0.679805\pi$
$228$	−1.31378	−	1.64375i	−0.0870070	−	0.108860i
$229$	−0.725435	+	0.725435i	−0.0479381	+	0.0479381i	−0.730669	−	0.682731i	$-0.760792\pi$
$229$	−0.725435	+	0.725435i	−0.0479381	+	0.0479381i	0.682731	+	0.730669i	$0.260792\pi$
$230$	3.05169	+	1.76190i	0.201223	+	0.116176i
$231$	−4.36498	−	3.21416i	−0.287194	−	0.211476i
$232$	−7.22973	−	1.93720i	−0.474655	−	0.127183i
$233$	−11.6818			−0.765300			−0.382650	−	0.923893i	$-0.624988\pi$
$233$	−11.6818			−0.765300			−0.382650	+	0.923893i	$0.624988\pi$
$234$	−3.76619	−	10.1398i	−0.246203	−	0.662860i
$235$	9.92018			0.647121
$236$	4.67330	+	1.25221i	0.304206	+	0.0815118i
$237$	−8.24220	−	6.06916i	−0.535388	−	0.394234i
$238$	2.14341	+	1.23750i	0.138936	+	0.0802150i
$239$	−14.3879	+	14.3879i	−0.930674	+	0.930674i	−0.997748	−	0.0670742i	$-0.978634\pi$
$239$	−14.3879	+	14.3879i	−0.930674	+	0.930674i	0.0670742	+	0.997748i	$0.478634\pi$
$240$	1.08139	+	1.35299i	0.0698035	+	0.0873354i
$241$	−4.66870	−	17.4238i	−0.300738	−	1.12237i	−0.936553	−	0.350527i	$-0.886003\pi$
$241$	−4.66870	−	17.4238i	−0.300738	−	1.12237i	0.635815	−	0.771841i	$-0.280664\pi$
$242$	2.39480	+	2.39480i	0.153944	+	0.153944i
$243$	15.5805	+	0.497989i	0.999490	+	0.0319460i
$244$	−11.9075	+	6.87481i	−0.762301	+	0.440115i
$245$	−1.63553	+	6.10387i	−0.104490	+	0.389962i
$246$	3.31760	+	7.58146i	0.211522	+	0.483376i
$247$	3.66916	−	2.39267i	0.233463	−	0.152242i
$248$		−	0.00393727i		−	0.000250017i
$249$	12.9864	−	1.97186i	0.822980	−	0.124962i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	14.7378	−	25.5266i	0.930242	−	1.61123i	0.147335	−	0.989087i	$-0.452930\pi$
$251$	14.7378	−	25.5266i	0.930242	−	1.61123i	0.782906	−	0.622139i	$-0.213736\pi$
$252$	2.47339	−	0.0979463i	0.155809	−	0.00617004i
$253$	−12.9103	+	3.45930i	−0.811662	+	0.217484i
$254$	−0.762676	+	0.204358i	−0.0478546	+	0.0128226i
$255$	1.89284	−	4.83837i	0.118534	−	0.302990i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.45733	−	11.1844i	−0.402797	−	0.697665i	0.591265	−	0.806477i	$-0.298629\pi$
$257$	−6.45733	−	11.1844i	−0.402797	−	0.697665i	−0.994062	+	0.108812i	$0.965295\pi$
$258$	1.02291	+	6.73675i	0.0636836	+	0.419411i
$259$		−	9.38739i		−	0.583304i
$260$	−3.02014	+	1.96945i	−0.187301	+	0.122140i
$261$	16.4934	+	15.2369i	1.02092	+	0.943140i
$262$	−0.159330	+	0.594626i	−0.00984342	+	0.0367361i
$263$	−23.8997	+	13.7985i	−1.47372	+	0.850850i	−0.999562	−	0.0295919i	$-0.990579\pi$
$263$	−23.8997	+	13.7985i	−1.47372	+	0.850850i	−0.474154	+	0.880442i	$0.657246\pi$
$264$	−6.52914	−	0.728453i	−0.401841	−	0.0448332i
$265$	3.46959	+	3.46959i	0.213135	+	0.213135i
$266$	0.259446	+	0.968265i	0.0159077	+	0.0593682i
$267$	−9.71525	+	7.76499i	−0.594564	+	0.475210i
$268$	−8.20679	+	8.20679i	−0.501309	+	0.501309i
$269$	18.1139	+	10.4581i	1.10442	+	0.637639i	0.937379	−	0.348310i	$-0.113244\pi$
$269$	18.1139	+	10.4581i	1.10442	+	0.637639i	0.167044	+	0.985949i	$0.446578\pi$
$270$	−0.982710	−	5.10238i	−0.0598058	−	0.310521i
$271$	−15.0716	−	4.03842i	−0.915534	−	0.245316i	−0.229858	−	0.973224i	$-0.573826\pi$
$271$	−15.0716	−	4.03842i	−0.915534	−	0.245316i	−0.685675	+	0.727908i	$0.740493\pi$
$272$	2.99959			0.181877
$273$	−0.292807	+	5.14449i	−0.0177215	+	0.311358i
$274$	−10.7262			−0.647991
$275$	3.66375	+	0.981698i	0.220932	+	0.0591986i
$276$	3.61896	−	4.91472i	0.217836	−	0.295831i
$277$	−21.0524	−	12.1546i	−1.26492	−	0.730301i	−0.290897	−	0.956754i	$-0.593954\pi$
$277$	−21.0524	−	12.1546i	−1.26492	−	0.730301i	−0.974022	+	0.226453i	$0.927287\pi$
$278$	−16.3906	+	16.3906i	−0.983042	+	0.983042i
$279$	−0.00549652	+	0.0104550i	−0.000329068	+	0.000625925i
$280$	−0.213554	−	0.796995i	−0.0127623	−	0.0476296i
$281$	−16.7143	−	16.7143i	−0.997090	−	0.997090i	0.00290627	−	0.999996i	$-0.499075\pi$
$281$	−16.7143	−	16.7143i	−0.997090	−	0.997090i	−0.999996	+	0.00290627i	$0.999075\pi$
$282$	1.90520	−	17.0763i	0.113453	−	1.01688i
$283$	19.5493	−	11.2868i	1.16208	−	0.670930i	0.210282	−	0.977641i	$-0.432562\pi$
$283$	19.5493	−	11.2868i	1.16208	−	0.670930i	0.951803	+	0.306711i	$0.0992285\pi$
$284$	−1.52747	+	5.70060i	−0.0906387	+	0.338268i
$285$	1.92777	−	0.843578i	0.114191	−	0.0499692i
$286$	2.81801	−	13.3823i	0.166632	−	0.791314i
$287$		−	3.94229i		−	0.232706i
$288$	2.53669	−	1.60163i	0.149476	−	0.0943769i
$289$	4.00123	+	6.93033i	0.235366	+	0.407666i
$290$	3.74239	−	6.48200i	0.219760	−	0.380636i
$291$	12.7863	+	5.00219i	0.749548	+	0.293234i
$292$	−11.5982	+	3.10772i	−0.678731	+	0.181865i
$293$	27.9435	−	7.48743i	1.63247	−	0.437420i	0.677843	−	0.735207i	$-0.262915\pi$
$293$	27.9435	−	7.48743i	1.63247	−	0.437420i	0.954632	+	0.297787i	$0.0962484\pi$
$294$	10.1929	+	3.98761i	0.594463	+	0.232562i
$295$	−2.41908	+	4.18997i	−0.140844	+	0.243949i
$296$	−5.68857	−	9.85289i	−0.330641	−	0.572688i
$297$	16.3205	+	11.0492i	0.947012	+	0.641137i
$298$		−	4.62556i		−	0.267952i
$299$	9.45790	+	8.48354i	0.546965	+	0.490616i
$300$	−1.58678	+	0.694363i	−0.0916126	+	0.0400891i
$301$	0.840132	−	3.13541i	0.0484244	−	0.180722i
$302$	6.44895	−	3.72330i	0.371095	−	0.214252i
$303$	2.95450	−	26.4813i	0.169732	−	1.52131i
$304$	0.859060	+	0.859060i	0.0492705	+	0.0492705i
$305$	−3.55867	−	13.2811i	−0.203769	−	0.760475i
$306$	−7.96510	−	4.18750i	−0.455334	−	0.239383i
$307$	−5.27808	+	5.27808i	−0.301236	+	0.301236i	−0.841497	−	0.540261i	$-0.818325\pi$
$307$	−5.27808	+	5.27808i	−0.301236	+	0.301236i	0.540261	+	0.841497i	$0.318325\pi$
$308$	2.71034	+	1.56482i	0.154436	+	0.0891637i
$309$	−16.8380	+	22.8668i	−0.957880	+	1.30085i
$310$	0.00380311	+	0.00101904i	0.000216002	+	5.78776e-5i
$311$	17.2916			0.980516			0.490258	−	0.871577i	$-0.336903\pi$
$311$	17.2916			0.980516			0.490258	+	0.871577i	$0.336903\pi$
$312$	2.81013	+	5.57702i	0.159092	+	0.315737i
$313$	−3.71423			−0.209941			−0.104970	−	0.994475i	$-0.533475\pi$
$313$	−3.71423			−0.209941			−0.104970	+	0.994475i	$0.533475\pi$
$314$	−4.21887	−	1.13044i	−0.238085	−	0.0637946i
$315$	−0.545552	+	2.41446i	−0.0307384	+	0.136040i
$316$	5.11782	+	2.95478i	0.287900	+	0.166219i
$317$	−11.8820	+	11.8820i	−0.667358	+	0.667358i	−0.957104	−	0.289746i	$-0.906429\pi$
$317$	−11.8820	+	11.8820i	−0.667358	+	0.667358i	0.289746	+	0.957104i	$0.406429\pi$
$318$	6.63879	−	5.30610i	0.372285	−	0.297551i
$319$	7.34778	+	27.4223i	0.411397	+	1.53535i
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$	1.34673	+	0.150255i	0.0751674	+	0.00838639i
$322$	−2.51798	+	1.45376i	−0.140322	+	0.0810148i
$323$	0.943185	−	3.52001i	0.0524802	−	0.195859i
$324$	−8.97182	+	0.711684i	−0.498434	+	0.0395380i
$325$	−1.12067	−	3.42697i	−0.0621637	−	0.190094i
$326$		−	5.09633i		−	0.282259i
$327$	0.185213	+	1.21979i	0.0102423	+	0.0674545i
$328$	−2.38895	−	4.13778i	−0.131908	−	0.228471i
$329$	−4.09262	+	7.08863i	−0.225634	+	0.390809i
$330$	2.39350	−	6.11813i	0.131758	−	0.336792i
$331$	−18.7857	+	5.03361i	−1.03256	+	0.276672i	−0.735025	−	0.678040i	$-0.762830\pi$
$331$	−18.7857	+	5.03361i	−1.03256	+	0.276672i	−0.297531	+	0.954712i	$0.596163\pi$
$332$	−7.32523	+	1.96279i	−0.402024	+	0.107722i
$333$	1.35055	+	34.1047i	0.0740094	+	1.86893i
$334$	−4.60993	+	7.98464i	−0.252244	+	0.436900i
$335$	−5.80308	−	10.0512i	−0.317056	−	0.549157i
$336$	−1.41294	+	0.214541i	−0.0770821	+	0.0117042i
$337$		−	29.4143i		−	1.60230i	−0.598465	−	0.801149i	$-0.704223\pi$
$337$		−	29.4143i		−	1.60230i	0.598465	−	0.801149i	$-0.295777\pi$
$338$	−12.1188	+	4.70474i	−0.659176	+	0.255904i
$339$	4.34265	+	9.92394i	0.235860	+	0.538994i
$340$	−0.776351	+	2.89738i	−0.0421036	+	0.157133i
$341$	−0.0129332	+	0.00746701i	−0.000700375	+	0.000404361i
$342$	−1.08188	−	3.48041i	−0.0585012	−	0.188199i
$343$	−7.77096	−	7.77096i	−0.419593	−	0.419593i
$344$	−1.01821	−	3.79999i	−0.0548980	−	0.204882i
$345$	3.81060	+	4.76767i	0.205156	+	0.256683i
$346$	3.88804	−	3.88804i	0.209023	−	0.209023i
$347$	−18.3677	−	10.6046i	−0.986030	−	0.569285i	−0.0819448	−	0.996637i	$-0.526113\pi$
$347$	−18.3677	−	10.6046i	−0.986030	−	0.569285i	−0.904085	+	0.427352i	$0.859446\pi$
$348$	−10.4392	−	7.68692i	−0.559599	−	0.412062i
$349$	−15.5273	−	4.16053i	−0.831157	−	0.222708i	−0.181939	−	0.983310i	$-0.558237\pi$
$349$	−15.5273	−	4.16053i	−0.831157	−	0.222708i	−0.649218	+	0.760602i	$0.724904\pi$
$350$	0.825110			0.0441040
$351$	0.323650	−	18.7322i	0.0172752	−	0.999851i
$352$	3.79299			0.202167
$353$	−31.5613	−	8.45683i	−1.67984	−	0.450112i	−0.712103	−	0.702075i	$-0.752257\pi$
$353$	−31.5613	−	8.45683i	−1.67984	−	0.450112i	−0.967737	+	0.251963i	$0.918924\pi$
$354$	6.74790	+	4.96882i	0.358647	+	0.264090i
$355$	−5.11102	−	2.95085i	−0.271265	−	0.156615i
$356$	5.07742	−	5.07742i	0.269103	−	0.269103i
$357$	2.67644	+	3.34865i	0.141652	+	0.177229i
$358$	1.24496	+	4.64624i	0.0657980	+	0.245562i
$359$	−4.78448	−	4.78448i	−0.252515	−	0.252515i	0.569486	−	0.822001i	$-0.307142\pi$
$359$	−4.78448	−	4.78448i	−0.252515	−	0.252515i	−0.822001	+	0.569486i	$0.807142\pi$
$360$	0.890511	+	2.86478i	0.0469341	+	0.150987i
$361$	−15.1763	+	8.76202i	−0.798750	+	0.461159i
$362$	−2.50725	+	9.35718i	−0.131778	+	0.491802i
$363$	2.35164	+	5.37404i	0.123429	+	0.282064i
$364$	−0.161327	−	2.97060i	−0.00845585	−	0.155702i
$365$		−	12.0073i		−	0.628490i
$366$	−23.5452	+	3.57511i	−1.23073	+	0.186874i
$367$	6.73485	+	11.6651i	0.351556	+	0.608913i	0.986522	−	0.163627i	$-0.0523192\pi$
$367$	6.73485	+	11.6651i	0.351556	+	0.608913i	−0.634966	+	0.772540i	$0.718986\pi$
$368$	−1.76190	+	3.05169i	−0.0918451	+	0.159080i
$369$	0.567170	+	14.3225i	0.0295257	+	0.745598i
$370$	10.9895	−	2.94462i	0.571315	−	0.153084i
$371$	−3.91065	+	1.04785i	−0.203031	+	0.0544019i
$372$	0.00248454	−	0.00635086i	0.000128818	−	0.000329277i
$373$	−17.0360	+	29.5072i	−0.882089	+	1.52782i	−0.0330743	+	0.999453i	$0.510530\pi$
$373$	−17.0360	+	29.5072i	−0.882089	+	1.52782i	−0.849014	+	0.528370i	$0.822804\pi$
$374$	−5.68871	−	9.85313i	−0.294156	−	0.509493i
$375$	−0.260015	−	1.71242i	−0.0134271	−	0.0884291i
$376$			9.92018i			0.511594i
$377$	18.0196	−	20.0892i	0.928057	−	1.03465i
$378$	4.05141	+	1.40280i	0.208382	+	0.0721523i
$379$	−6.18511	+	23.0832i	−0.317708	+	1.18570i	0.603734	+	0.797186i	$0.293679\pi$
$379$	−6.18511	+	23.0832i	−0.317708	+	1.18570i	−0.921442	+	0.388516i	$0.872988\pi$
$380$	−1.05213	+	0.607447i	−0.0539731	+	0.0311614i
$381$	−1.35916	−	0.151641i	−0.0696319	−	0.00776880i
$382$	−3.71699	−	3.71699i	−0.190178	−	0.190178i
$383$	5.87449	+	21.9239i	0.300172	+	1.12026i	0.937022	+	0.349270i	$0.113570\pi$
$383$	5.87449	+	21.9239i	0.300172	+	1.12026i	−0.636850	+	0.770988i	$0.719763\pi$
$384$	−1.35299	+	1.08139i	−0.0690447	+	0.0551845i
$385$	−2.21299	+	2.21299i	−0.112784	+	0.112784i
$386$	0.152621	+	0.0881160i	0.00776822	+	0.00448499i
$387$	−2.60114	+	11.5119i	−0.132223	+	0.585184i
$388$	−7.65690	−	2.05166i	−0.388720	−	0.104157i
$389$	−9.80108			−0.496934			−0.248467	−	0.968640i	$-0.579927\pi$
$389$	−9.80108			−0.496934			−0.248467	+	0.968640i	$0.579927\pi$
$390$	−6.11430	+	1.27093i	−0.309610	+	0.0643563i
$391$	10.5699			0.534544
$392$	−6.10387	−	1.63553i	−0.308292	−	0.0826066i
$393$	−0.632228	+	0.858596i	−0.0318917	+	0.0433104i
$394$	−6.33488	−	3.65744i	−0.319147	−	0.184259i
$395$	−4.17869	+	4.17869i	−0.210252	+	0.210252i
$396$	−10.0719	−	5.29510i	−0.506131	−	0.266089i
$397$	6.48832	+	24.2147i	0.325640	+	1.21530i	0.913667	+	0.406463i	$0.133238\pi$
$397$	6.48832	+	24.2147i	0.325640	+	1.21530i	−0.588028	+	0.808841i	$0.700095\pi$
$398$	13.8085	+	13.8085i	0.692160	+	0.692160i
$399$	−0.192518	+	1.72554i	−0.00963794	+	0.0863850i
$400$	0.866025	−	0.500000i	0.0433013	−	0.0250000i
$401$	8.23082	−	30.7179i	0.411028	−	1.53398i	−0.381633	−	0.924314i	$-0.624638\pi$
$401$	8.23082	−	30.7179i	0.411028	−	1.53398i	0.792661	−	0.609663i	$-0.208695\pi$
$402$	−18.4164	+	8.05888i	−0.918525	+	0.401940i
$403$	0.0126609	+	0.00642089i	0.000630687	+	0.000319847i
$404$			15.3838i			0.765374i
$405$	1.63464	−	8.85031i	0.0812261	−	0.439775i
$406$	3.08788	+	5.34837i	0.153249	+	0.265435i
$407$	−21.5767	+	37.3719i	−1.06952	+	1.85246i
$408$	4.83837	+	1.89284i	0.239535	+	0.0937094i
$409$	21.7307	−	5.82273i	1.07451	−	0.287915i	0.322168	−	0.946683i	$-0.395588\pi$
$409$	21.7307	−	5.82273i	1.07451	−	0.287915i	0.752347	+	0.658767i	$0.228922\pi$
$410$	4.61510	−	1.23661i	0.227923	−	0.0610719i
$411$	−17.3014	−	6.76854i	−0.853414	−	0.333868i
$412$	8.19760	−	14.1987i	0.403867	−	0.699518i
$413$	−1.99601	−	3.45719i	−0.0982171	−	0.170117i
$414$	8.93876	−	5.64380i	0.439316	−	0.277378i
$415$		−	7.58364i		−	0.372266i
$416$	−1.96945	−	3.02014i	−0.0965602	−	0.148075i
$417$	−36.7812	+	16.0952i	−1.80118	+	0.788185i
$418$	1.19266	−	4.45107i	0.0583349	−	0.217709i
$419$	16.2904	−	9.40527i	0.795838	−	0.459477i	−0.0461757	−	0.998933i	$-0.514703\pi$
$419$	16.2904	−	9.40527i	0.795838	−	0.459477i	0.842014	+	0.539456i	$0.181370\pi$
$420$	0.158464	−	1.42032i	0.00773228	−	0.0693045i
$421$	22.9593	+	22.9593i	1.11897	+	1.11897i	0.991893	+	0.127075i	$0.0405590\pi$
$421$	22.9593	+	22.9593i	1.11897	+	1.11897i	0.127075	+	0.991893i	$0.459441\pi$
$422$	1.57667	+	5.88420i	0.0767510	+	0.286439i
$423$	13.8488	−	26.3420i	0.673351	−	1.28079i
$424$	−3.46959	+	3.46959i	−0.168498	+	0.168498i
$425$	−2.59772	−	1.49980i	−0.126008	−	0.0727508i
$426$	−6.06109	+	8.23124i	−0.293661	+	0.398805i
$427$	10.9584	+	2.93629i	0.530314	+	0.142097i
$428$	−0.782362			−0.0378169
$429$	12.9902	−	19.8076i	0.627170	−	0.956318i
$430$	3.93404			0.189716
$431$	21.1395	+	5.66432i	1.01825	+	0.272840i	0.729075	−	0.684434i	$-0.239951\pi$
$431$	21.1395	+	5.66432i	1.01825	+	0.272840i	0.289180	+	0.957275i	$0.406617\pi$
$432$	5.10238	−	0.982710i	0.245488	−	0.0472807i
$433$	−5.85090	−	3.37802i	−0.281176	−	0.162337i	0.352779	−	0.935707i	$-0.385237\pi$
$433$	−5.85090	−	3.37802i	−0.281176	−	0.162337i	−0.633956	+	0.773369i	$0.718570\pi$
$434$	−0.00229717	+	0.00229717i	−0.000110267	+	0.000110267i
$435$	10.1269	−	8.09396i	0.485545	−	0.388076i
$436$	−0.184361	−	0.688046i	−0.00882931	−	0.0329515i
$437$	3.02715	+	3.02715i	0.144808	+	0.144808i
$438$	−20.6690	−	2.30603i	−0.987603	−	0.110186i
$439$	−23.5242	+	13.5817i	−1.12275	+	0.648219i	−0.942101	−	0.335329i	$-0.891153\pi$
$439$	−23.5242	+	13.5817i	−1.12275	+	0.648219i	−0.180648	+	0.983548i	$0.557819\pi$
$440$	−0.981698	+	3.66375i	−0.0468006	+	0.174662i
$441$	13.9250	+	12.8641i	0.663093	+	0.612577i
$442$	−4.89172	+	9.64568i	−0.232675	+	0.458798i
$443$		−	30.5438i		−	1.45118i	−0.688126	−	0.725591i	$-0.741566\pi$
$443$		−	30.5438i		−	1.45118i	0.688126	−	0.725591i	$-0.258434\pi$
$444$	−2.95823	−	19.4825i	−0.140391	−	0.924597i
$445$	3.59028	+	6.21854i	0.170195	+	0.294787i
$446$	4.15595	−	7.19831i	0.196790	−	0.340850i
$447$	2.91888	−	7.46108i	0.138058	−	0.352897i
$448$	0.796995	−	0.213554i	0.0376545	−	0.0100895i
$449$	−14.7387	+	3.94923i	−0.695563	+	0.186376i	−0.589242	−	0.807956i	$-0.700574\pi$
$449$	−14.7387	+	3.94923i	−0.695563	+	0.186376i	−0.106321	+	0.994332i	$0.533907\pi$
$450$	−2.99765	+	0.118707i	−0.141311	+	0.00559590i
$451$	−9.06126	+	15.6946i	−0.426678	+	0.739028i
$452$	−3.12708	−	5.41625i	−0.147085	−	0.254759i
$453$	12.7517	−	1.93623i	0.599129	−	0.0909720i
$454$		−	20.4099i		−	0.957886i
$455$	2.91113	+	0.613018i	0.136476	+	0.0287387i
$456$	0.843578	+	1.92777i	0.0395041	+	0.0902759i
$457$	0.951818	−	3.55223i	0.0445242	−	0.166167i	−0.940084	−	0.340943i	$-0.889254\pi$
$457$	0.951818	−	3.55223i	0.0445242	−	0.166167i	0.984608	+	0.174777i	$0.0559203\pi$
$458$	0.888473	−	0.512960i	0.0415156	−	0.0239690i
$459$	−10.2053	−	11.7807i	−0.476344	−	0.549876i
$460$	−2.49170	−	2.49170i	−0.116176	−	0.116176i
$461$	−4.95099	−	18.4773i	−0.230591	−	0.860576i	−0.980087	−	0.198568i	$-0.936371\pi$
$461$	−4.95099	−	18.4773i	−0.230591	−	0.860576i	0.749497	−	0.662008i	$-0.230296\pi$
$462$	3.38436	+	4.23438i	0.157455	+	0.197001i
$463$	28.1621	−	28.1621i	1.30880	−	1.30880i	0.386523	−	0.922280i	$-0.373676\pi$
$463$	28.1621	−	28.1621i	1.30880	−	1.30880i	0.922280	−	0.386523i	$-0.126324\pi$
$464$	6.48200	+	3.74239i	0.300919	+	0.173736i
$465$	0.00549141	+	0.00404361i	0.000254658	+	0.000187518i
$466$	11.2837	+	3.02347i	0.522709	+	0.140060i
$467$	31.6851			1.46621			0.733105	−	0.680116i	$-0.238070\pi$
$467$	31.6851			1.46621			0.733105	+	0.680116i	$0.238070\pi$
$468$	1.01348	+	10.7691i	0.0468482	+	0.497800i
$469$	9.57635			0.442195
$470$	−9.58216	−	2.56753i	−0.441992	−	0.118431i
$471$	−6.09173	−	4.48566i	−0.280692	−	0.206688i
$472$	−4.18997	−	2.41908i	−0.192859	−	0.111347i
$473$	−10.5513	+	10.5513i	−0.485149	+	0.485149i
$474$	6.39054	+	7.99559i	0.293527	+	0.367250i
$475$	−0.314438	−	1.17350i	−0.0144274	−	0.0538438i
$476$	−1.75008	−	1.75008i	−0.0802150	−	0.0802150i
$477$	14.0567	−	4.36950i	0.643614	−	0.200066i
$478$	17.6215	−	10.1738i	0.805987	−	0.465337i
$479$	6.64561	−	24.8018i	0.303646	−	1.13322i	−0.630459	−	0.776222i	$-0.717133\pi$
$479$	6.64561	−	24.8018i	0.303646	−	1.13322i	0.934105	−	0.356999i	$-0.116200\pi$
$480$	−0.694363	−	1.58678i	−0.0316932	−	0.0724261i
$481$	40.9605	−	2.22448i	1.86764	−	0.101428i
$482$			18.0385i			0.821631i
$483$	−4.97890	+	0.755998i	−0.226548	+	0.0343991i
$484$	−1.69338	−	2.93302i	−0.0769719	−	0.133319i
$485$	3.96350	−	6.86499i	0.179973	−	0.311723i
$486$	−14.9207	−	4.51355i	−0.676818	−	0.204739i
$487$	−23.2525	+	6.23048i	−1.05367	+	0.282330i	−0.743768	−	0.668438i	$-0.766963\pi$
$487$	−23.2525	+	6.23048i	−1.05367	+	0.282330i	−0.309903	+	0.950768i	$0.600297\pi$
$488$	13.2811	−	3.55867i	0.601208	−	0.161093i
$489$	3.21594	−	8.22042i	0.145430	−	0.371740i
$490$	3.15960	−	5.47258i	0.142736	−	0.247226i
$491$	5.01301	+	8.68279i	0.226234	+	0.391849i	0.956689	−	0.291112i	$-0.0940252\pi$
$491$	5.01301	+	8.68279i	0.226234	+	0.391849i	−0.730455	+	0.682961i	$0.760692\pi$
$492$	−1.24233	−	8.18178i	−0.0560083	−	0.368863i
$493$		−	22.4512i		−	1.01115i
$494$	−4.16340	+	1.36150i	−0.187320	+	0.0612567i
$495$	7.72146	−	8.35822i	0.347054	−	0.375674i
$496$	−0.00101904	+	0.00380311i	−4.57563e−5	+	0.000170765i
$497$	4.21715	−	2.43477i	0.189165	−	0.109215i
$498$	−13.0543	−	1.45646i	−0.584975	−	0.0652654i
$499$	−15.2170	−	15.2170i	−0.681206	−	0.681206i	0.279066	−	0.960272i	$-0.409975\pi$
$499$	−15.2170	−	15.2170i	−0.681206	−	0.681206i	−0.960272	+	0.279066i	$0.909975\pi$
$500$	0.258819	+	0.965926i	0.0115747	+	0.0431975i
$501$	−12.4744	+	9.97028i	−0.557316	+	0.445439i
$502$	−20.8424	+	20.8424i	−0.930242	+	0.930242i
$503$	30.8229	+	17.7956i	1.37433	+	0.793467i	0.991469	−	0.130341i	$-0.0416071\pi$
$503$	30.8229	+	17.7956i	1.37433	+	0.793467i	0.382856	+	0.923808i	$0.374940\pi$
$504$	−2.41446	−	0.545552i	−0.107549	−	0.0243008i
$505$	−14.8596	−	3.98163i	−0.661245	−	0.177180i
$506$	13.3657			0.594178
$507$	−22.5166	−	0.0585567i	−0.999997	−	0.00260059i
$508$	0.789580			0.0350320
$509$	−25.7113	−	6.88933i	−1.13963	−	0.305364i	−0.360830	−	0.932632i	$-0.617507\pi$
$509$	−25.7113	−	6.88933i	−1.13963	−	0.305364i	−0.778804	+	0.627267i	$0.784173\pi$
$510$	−3.08060	+	4.18360i	−0.136411	+	0.185253i
$511$	8.58001	+	4.95367i	0.379557	+	0.219137i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	0.451173	−	6.29664i	0.0199198	−	0.278003i
$514$	3.34256	+	12.4746i	0.147434	+	0.550231i
$515$	11.5932	+	11.5932i	0.510855	+	0.510855i
$516$	0.755543	−	6.77195i	0.0332609	−	0.298118i
$517$	32.5861	−	18.8136i	1.43313	−	0.827420i
$518$	−2.42964	+	9.06753i	−0.106752	+	0.398404i
$519$	8.72493	−	3.81797i	0.382982	−	0.167590i
$520$	3.42697	−	1.12067i	0.150282	−	0.0491447i
$521$			13.4752i			0.590358i	0.955442	+	0.295179i	$0.0953793\pi$
$521$			13.4752i			0.590358i	−0.955442	+	0.295179i	$0.904621\pi$
$522$	−11.9878	−	18.9865i	−0.524693	−	0.831018i
$523$	2.98474	+	5.16972i	0.130514	+	0.226056i	0.923875	−	0.382695i	$-0.125004\pi$
$523$	2.98474	+	5.16972i	0.130514	+	0.226056i	−0.793361	+	0.608751i	$0.791671\pi$
$524$	0.307801	−	0.533127i	0.0134464	−	0.0232898i
$525$	1.33091	+	0.520671i	0.0580857	+	0.0227239i
$526$	26.6566	−	7.14261i	1.16228	−	0.311433i
$527$	0.0114078	−	0.00305671i	0.000496931	−	0.000133152i
$528$	6.11813	+	2.39350i	0.266257	+	0.104164i
$529$	5.29145	−	9.16506i	0.230063	−	0.398481i
$530$	−2.45337	−	4.24936i	−0.106567	−	0.184580i
$531$	7.74893	+	12.2729i	0.336275	+	0.532598i
$532$		−	1.00242i		−	0.0434605i
$533$	17.2016	−	0.934185i	0.745084	−	0.0404641i
$534$	11.3939	−	4.98591i	0.493064	−	0.215761i
$535$	0.202490	−	0.755704i	0.00875441	−	0.0326719i
$536$	10.0512	−	5.80308i	0.434147	−	0.250655i
$537$	−0.923801	+	8.28004i	−0.0398649	+	0.357310i
$538$	−14.7899	−	14.7899i	−0.637639	−	0.637639i
$539$	6.20354	+	23.1519i	0.267205	+	0.997224i
$540$	−0.371368	+	5.18286i	−0.0159811	+	0.223035i
$541$	22.2468	−	22.2468i	0.956465	−	0.956465i	−0.0426256	−	0.999091i	$-0.513572\pi$
$541$	22.2468	−	22.2468i	0.956465	−	0.956465i	0.999091	+	0.0426256i	$0.0135723\pi$
$542$	13.5128	+	7.80163i	0.580425	+	0.335109i
$543$	−9.94889	+	13.5111i	−0.426948	+	0.579815i
$544$	−2.89738	−	0.776351i	−0.124224	−	0.0332858i
$545$	0.712318			0.0305124
$546$	1.61432	−	4.89341i	0.0690865	−	0.209419i
$547$	−23.4492			−1.00261			−0.501307	−	0.865269i	$-0.667147\pi$
$547$	−23.4492			−1.00261			−0.501307	+	0.865269i	$0.667147\pi$
$548$	10.3607	+	2.77613i	0.442586	+	0.118590i
$549$	−40.2346	−	9.09108i	−1.71717	−	0.387998i
$550$	−3.28482	−	1.89649i	−0.140065	−	0.0808668i
$551$	6.42987	−	6.42987i	0.273922	−	0.273922i
$552$	−4.76767	+	3.81060i	−0.202925	+	0.162190i
$553$	−1.26201	−	4.70989i	−0.0536661	−	0.200285i
$554$	17.1892	+	17.1892i	0.730301	+	0.730301i
$555$	19.5843	+	2.18501i	0.831306	+	0.0927484i
$556$	20.0743	−	11.5899i	0.851340	−	0.491521i
$557$	−0.216431	+	0.807730i	−0.00917046	+	0.0342246i	−0.970359	−	0.241666i	$-0.922306\pi$
$557$	−0.216431	+	0.807730i	−0.00917046	+	0.0342246i	0.961189	+	0.275891i	$0.0889728\pi$
$558$	0.00801519	−	0.00867616i	0.000339310	−	0.000367291i
$559$	13.8800	+	2.92281i	0.587061	+	0.123622i
$560$			0.825110i			0.0348673i
$561$	−2.95830	−	19.4829i	−0.124899	−	0.822571i
$562$	11.8188	+	20.4707i	0.498545	+	0.863505i
$563$	−15.1333	+	26.2117i	−0.637794	+	1.10469i	0.348122	+	0.937449i	$0.386820\pi$
$563$	−15.1333	+	26.2117i	−0.637794	+	1.10469i	−0.985916	+	0.167242i	$0.946514\pi$
$564$	−6.25995	+	16.0013i	−0.263592	+	0.673778i
$565$	6.04105	−	1.61869i	0.254149	−	0.0680989i
$566$	−21.8044	+	5.84247i	−0.916507	+	0.245577i
$567$	5.64975	+	4.81930i	0.237267	+	0.202392i
$568$	2.95085	−	5.11102i	0.123815	−	0.214454i
$569$	−6.86965	−	11.8986i	−0.287991	−	0.498814i	0.685339	−	0.728224i	$-0.259654\pi$
$569$	−6.86965	−	11.8986i	−0.287991	−	0.498814i	−0.973330	+	0.229409i	$0.926321\pi$
$570$	−2.08041	+	0.315891i	−0.0871389	+	0.0132312i
$571$			26.2679i			1.09928i	0.835403	+	0.549638i	$0.185235\pi$
$571$			26.2679i			1.09928i	−0.835403	+	0.549638i	$0.814765\pi$
$572$	−6.18559	+	12.1970i	−0.258633	+	0.509981i
$573$	−3.65000	−	8.34108i	−0.152481	−	0.348454i
$574$	−1.02034	+	3.80796i	−0.0425882	+	0.158941i
$575$	3.05169	−	1.76190i	0.127264	−	0.0734761i
$576$	−2.86478	+	0.890511i	−0.119366	+	0.0371046i
$577$	17.6073	+	17.6073i	0.733000	+	0.733000i	0.971213	−	0.238213i	$-0.0765617\pi$
$577$	17.6073	+	17.6073i	0.733000	+	0.733000i	−0.238213	+	0.971213i	$0.576562\pi$
$578$	−2.07119	−	7.72978i	−0.0861500	−	0.321516i
$579$	0.190576	+	0.238441i	0.00792005	+	0.00990926i
$580$	−5.29253	+	5.29253i	−0.219760	+	0.219760i
$581$	5.41901	+	3.12867i	0.224819	+	0.129799i
$582$	−11.0560	−	8.14109i	−0.458285	−	0.337459i
$583$	17.9770	+	4.81693i	0.744533	+	0.199497i
$584$	12.0073			0.496865
$585$	−10.6644	−	1.80829i	−0.440920	−	0.0747637i
$586$	−28.9292			−1.19505
$587$	−6.50869	−	1.74400i	−0.268643	−	0.0719826i	0.121983	−	0.992532i	$-0.461075\pi$
$587$	−6.50869	−	1.74400i	−0.268643	−	0.0719826i	−0.390626	+	0.920550i	$0.627741\pi$
$588$	−8.81353	−	6.48986i	−0.363464	−	0.267637i
$589$	0.00414252	+	0.00239169i	0.000170690	+	9.85477e-5i
$590$	3.42109	−	3.42109i	0.140844	−	0.140844i
$591$	−7.91025	−	9.89700i	−0.325384	−	0.407108i
$592$	2.94462	+	10.9895i	0.121023	+	0.451665i
$593$	−22.4859	−	22.4859i	−0.923387	−	0.923387i	0.0738801	−	0.997267i	$-0.476462\pi$
$593$	−22.4859	−	22.4859i	−0.923387	−	0.923387i	−0.997267	+	0.0738801i	$0.976462\pi$
$594$	−12.9047	−	14.8967i	−0.529485	−	0.611220i
$595$	2.14341	−	1.23750i	0.0878711	−	0.0507324i
$596$	−1.19718	+	4.46795i	−0.0490386	+	0.183014i
$597$	13.5597	+	30.9870i	0.554961	+	1.26821i
$598$	−6.93993	−	10.6424i	−0.283795	−	0.435198i
$599$			20.4003i			0.833532i	0.909014	+	0.416766i	$0.136837\pi$
$599$			20.4003i			0.833532i	−0.909014	+	0.416766i	$0.863163\pi$
$600$	1.71242	−	0.260015i	0.0699094	−	0.0106151i
$601$	6.60632	+	11.4425i	0.269477	+	0.466749i	0.968727	−	0.248129i	$-0.0798157\pi$
$601$	6.60632	+	11.4425i	0.269477	+	0.466749i	−0.699250	+	0.714878i	$0.746482\pi$
$602$	−1.62301	+	2.81114i	−0.0661489	+	0.114573i
$603$	−34.7912	+	1.37773i	−1.41681	+	0.0561055i
$604$	−7.19287	+	1.92732i	−0.292674	+	0.0784217i
$605$	3.27136	−	0.876559i	0.133000	−	0.0356372i
$606$	−9.70769	+	24.8143i	−0.394348	+	1.00801i
$607$	2.52615	−	4.37542i	0.102533	−	0.177593i	−0.810195	−	0.586161i	$-0.800639\pi$
$607$	2.52615	−	4.37542i	0.102533	−	0.177593i	0.912728	+	0.408568i	$0.133972\pi$
$608$	−0.607447	−	1.05213i	−0.0246352	−	0.0426695i
$609$	1.60579	+	10.5755i	0.0650699	+	0.428541i
$610$			13.7496i			0.556706i
$611$	−31.9000	−	16.1778i	−1.29054	−	0.654483i
$612$	6.60989	+	6.10633i	0.267189	+	0.246834i
$613$	−3.28773	+	12.2700i	−0.132790	+	0.495579i	−0.999997	−	0.00236831i	$-0.999246\pi$
$613$	−3.28773	+	12.2700i	−0.132790	+	0.495579i	0.867207	+	0.497948i	$0.165913\pi$
$614$	6.46430	−	3.73217i	0.260878	−	0.150618i
$615$	8.22453	+	0.917607i	0.331645	+	0.0370015i
$616$	−2.21299	−	2.21299i	−0.0891637	−	0.0891637i
$617$	−1.98367	−	7.40316i	−0.0798596	−	0.298040i	0.914432	−	0.404740i	$-0.132638\pi$
$617$	−1.98367	−	7.40316i	−0.0798596	−	0.298040i	−0.994291	+	0.106700i	$0.965971\pi$
$618$	22.1826	−	17.7296i	0.892315	−	0.713190i
$619$	20.2426	−	20.2426i	0.813620	−	0.813620i	−0.171555	−	0.985175i	$-0.554879\pi$
$619$	20.2426	−	20.2426i	0.813620	−	0.813620i	0.985175	+	0.171555i	$0.0548791\pi$
$620$	−0.00340978	−	0.00196864i	−0.000136940	−	7.90623e-5i
$621$	17.9797	−	3.46287i	0.721501	−	0.138960i
$622$	−16.7024	−	4.47539i	−0.669705	−	0.179447i
$623$	−5.92475			−0.237370
$624$	−1.27093	−	6.11430i	−0.0508781	−	0.244768i
$625$	−1.00000			−0.0400000
$626$	3.58767	+	0.961314i	0.143392	+	0.0384218i
$627$	4.73254	−	6.42700i	0.188999	−	0.256670i
$628$	3.78254	+	2.18385i	0.150940	+	0.0871450i
$629$	24.1313	−	24.1313i	0.962177	−	0.962177i
$630$	1.15187	−	2.19099i	0.0458917	−	0.0872913i
$631$	−5.56480	−	20.7681i	−0.221531	−	0.826766i	−0.983765	−	0.179464i	$-0.942564\pi$
$631$	−5.56480	−	20.7681i	−0.221531	−	0.826766i	0.762233	−	0.647302i	$-0.224103\pi$
$632$	−4.17869	−	4.17869i	−0.166219	−	0.166219i
$633$	−1.16994	+	10.4862i	−0.0465010	+	0.416789i
$634$	14.5524	−	8.40182i	0.577949	−	0.333679i
$635$	−0.204358	+	0.762676i	−0.00810972	+	0.0302659i
$636$	−7.78589	+	3.40705i	−0.308731	+	0.135099i
$637$	15.2135	−	16.9608i	0.602780	−	0.672011i
$638$		−	28.3896i		−	1.12396i
$639$	−14.9708	+	9.45232i	−0.592234	+	0.373928i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−17.0880	+	29.5973i	−0.674936	+	1.16902i	0.301552	+	0.953450i	$0.402495\pi$
$641$	−17.0880	+	29.5973i	−0.674936	+	1.16902i	−0.976488	+	0.215573i	$0.930838\pi$
$642$	−1.26196	−	0.493695i	−0.0498055	−	0.0194846i
$643$	29.1672	−	7.81533i	1.15024	−	0.308206i	0.367180	−	0.930150i	$-0.380323\pi$
$643$	29.1672	−	7.81533i	1.15024	−	0.308206i	0.783062	+	0.621943i	$0.213657\pi$
$644$	2.80844	−	0.752520i	0.110668	−	0.0296535i
$645$	6.34565	+	2.48251i	0.249860	+	0.0977486i
$646$	−1.82209	+	3.15596i	−0.0716893	+	0.124170i
$647$	16.6435	+	28.8275i	0.654325	+	1.13332i	0.982063	+	0.188555i	$0.0603805\pi$
$647$	16.6435	+	28.8275i	0.654325	+	1.13332i	−0.327737	+	0.944769i	$0.606286\pi$
$648$	8.85031	+	1.63464i	0.347673	+	0.0642149i
$649$			18.3511i			0.720343i
$650$	0.195522	+	3.60025i	0.00766901	+	0.141213i
$651$	−0.00515493	+	0.00225576i	−0.000202038	+	8.84104e-5i
$652$	−1.31903	+	4.92267i	−0.0516571	+	0.192787i
$653$	−38.8066	+	22.4050i	−1.51862	+	0.876776i	−0.518860	+	0.854859i	$0.673644\pi$
$653$	−38.8066	+	22.4050i	−1.51862	+	0.876776i	−0.999760	+	0.0219166i	$0.993023\pi$
$654$	0.136802	−	1.22616i	0.00534940	−	0.0479468i
$655$	0.435297	+	0.435297i	0.0170085	+	0.0170085i
$656$	1.23661	+	4.61510i	0.0482816	+	0.180189i
$657$	−31.8841	−	16.7624i	−1.24392	−	0.653965i
$658$	5.78784	−	5.78784i	0.225634	−	0.225634i
$659$	−15.8615	−	9.15765i	−0.617877	−	0.356731i	0.158165	−	0.987413i	$-0.449442\pi$
$659$	−15.8615	−	9.15765i	−0.617877	−	0.356731i	−0.776042	+	0.630681i	$0.782775\pi$
$660$	−3.89543	+	5.29017i	−0.151629	+	0.205920i
$661$	−46.0633	−	12.3426i	−1.79165	−	0.480072i	−0.799029	−	0.601293i	$-0.794653\pi$
$661$	−46.0633	−	12.3426i	−1.79165	−	0.480072i	−0.992626	+	0.121221i	$0.961319\pi$
$662$	19.4484			0.755883
$663$	−13.9771	+	12.4717i	−0.542826	+	0.484362i
$664$	7.58364			0.294302
$665$	0.968265	+	0.259446i	0.0375477	+	0.0100609i
$666$	7.52242	−	33.2921i	0.291488	−	1.29004i
$667$	22.8412	+	13.1874i	0.884415	+	0.510617i
$668$	6.51943	−	6.51943i	0.252244	−	0.252244i
$669$	11.2459	−	8.98840i	0.434793	−	0.347512i
$670$	3.00389	+	11.2107i	0.116051	+	0.433106i
$671$	−36.8772	−	36.8772i	−1.42363	−	1.42363i
$672$	1.42032	+	0.158464i	0.0547900	+	0.00611290i
$673$	23.3095	−	13.4577i	0.898514	−	0.518757i	0.0217965	−	0.999762i	$-0.493061\pi$
$673$	23.3095	−	13.4577i	0.898514	−	0.518757i	0.876718	+	0.481005i	$0.159728\pi$
$674$	−7.61297	+	28.4120i	−0.293241	+	1.09439i
$675$	−4.91015	−	1.70014i	−0.188992	−	0.0654383i
$676$	12.9235	−	1.40786i	0.497059	−	0.0541483i
$677$			35.2263i			1.35385i	0.736050	+	0.676927i	$0.236689\pi$
$677$			35.2263i			1.35385i	−0.736050	+	0.676927i	$0.763311\pi$
$678$	−1.62617	−	10.7097i	−0.0624528	−	0.411305i
$679$	3.27033	+	5.66437i	0.125504	+	0.217379i
$680$	1.49980	−	2.59772i	0.0575145	−	0.0996181i
$681$	12.8793	−	32.9214i	0.493537	−	1.26155i
$682$	0.0144252	−	0.00386521i	0.000552368	−	0.000148007i
$683$	25.9255	−	6.94671i	0.992010	−	0.265808i	0.273915	−	0.961754i	$-0.411681\pi$
$683$	25.9255	−	6.94671i	0.992010	−	0.265808i	0.718095	+	0.695945i	$0.245014\pi$
$684$	0.144216	+	3.64183i	0.00551425	+	0.139249i
$685$	−5.36308	+	9.28912i	−0.204913	+	0.354919i
$686$	5.49490	+	9.51745i	0.209796	+	0.363378i
$687$	1.75681	−	0.266755i	0.0670264	−	0.0101773i
$688$			3.93404i			0.149984i
$689$	−5.49884	−	16.8152i	−0.209489	−	0.640609i
$690$	−2.44679	−	5.59147i	−0.0931477	−	0.212864i
$691$	−3.82546	+	14.2768i	−0.145527	+	0.543116i	0.854204	+	0.519938i	$0.174045\pi$
$691$	−3.82546	+	14.2768i	−0.145527	+	0.543116i	−0.999731	+	0.0231778i	$0.992622\pi$
$692$	−4.76186	+	2.74926i	−0.181019	+	0.104511i
$693$	2.78697	+	8.96573i	0.105868	+	0.340580i
$694$	14.9972	+	14.9972i	0.569285	+	0.569285i
$695$	5.99937	+	22.3900i	0.227569	+	0.849300i
$696$	8.09396	+	10.1269i	0.306801	+	0.383857i
$697$	10.1341	−	10.1341i	0.383855	−	0.383855i
$698$	13.9214	+	8.03752i	0.526932	+	0.304225i
$699$	16.2929	+	11.9973i	0.616253	+	0.453779i
$700$	−0.796995	−	0.213554i	−0.0301236	−	0.00807159i
$701$	19.3599			0.731215			0.365608	−	0.930769i	$-0.380861\pi$
$701$	19.3599			0.731215			0.365608	+	0.930769i	$0.380861\pi$
$702$	−5.16087	+	18.0101i	−0.194785	+	0.679749i
$703$	13.8220			0.521308
$704$	−3.66375	−	0.981698i	−0.138083	−	0.0369991i
$705$	−13.8359	−	10.1881i	−0.521091	−	0.383706i
$706$	28.2971	+	16.3373i	1.06498	+	0.614864i
$707$	8.97556	−	8.97556i	0.337561	−	0.337561i
$708$	−5.23194	−	6.54600i	−0.196628	−	0.246014i
$709$	7.45717	+	27.8305i	0.280060	+	1.04520i	0.952374	+	0.304932i	$0.0986338\pi$
$709$	7.45717	+	27.8305i	0.280060	+	1.04520i	−0.672314	+	0.740266i	$0.734700\pi$
$710$	4.17313	+	4.17313i	0.156615	+	0.156615i
$711$	5.26252	+	16.9296i	0.197360	+	0.634909i
$712$	−6.21854	+	3.59028i	−0.233050	+	0.134551i
$713$	−0.00359089	+	0.0134014i	−0.000134480	+	0.000501885i
$714$	−1.71854	−	3.92726i	−0.0643149	−	0.146974i
$715$	−10.1804	−	9.13163i	−0.380727	−	0.341504i
$716$		−	4.81015i		−	0.179764i
$717$	34.8436	−	5.29066i	1.30126	−	0.197583i
$718$	3.38314	+	5.85977i	0.126258	+	0.218685i
$719$	−3.77091	+	6.53140i	−0.140631	+	0.243580i	−0.927734	−	0.373241i	$-0.878246\pi$
$719$	−3.77091	+	6.53140i	−0.140631	+	0.243580i	0.787103	+	0.616821i	$0.211580\pi$
$720$	−0.118707	−	2.99765i	−0.00442395	−	0.111716i
$721$	−13.0669	+	3.50126i	−0.486637	+	0.130394i
$722$	16.9269	−	4.53555i	0.629955	−	0.168796i
$723$	−11.3829	+	29.0962i	−0.423333	+	1.08210i
$724$	4.84363	−	8.38941i	0.180012	−	0.311790i
$725$	−3.74239	−	6.48200i	−0.138989	−	0.240735i
$726$	−0.880609	−	5.79957i	−0.0326825	−	0.215242i
$727$		−	18.8445i		−	0.698904i	−0.936954	−	0.349452i	$-0.886368\pi$
$727$		−	18.8445i		−	0.698904i	0.936954	−	0.349452i	$-0.113632\pi$
$728$	−0.613018	+	2.91113i	−0.0227199	+	0.107894i
$729$	−21.2191	−	16.6958i	−0.785891	−	0.618365i
$730$	−3.10772	+	11.5982i	−0.115022	+	0.429267i
$731$	10.2196	−	5.90026i	0.377984	−	0.218229i
$732$	23.6682	+	2.64065i	0.874802	+	0.0976013i
$733$	−26.3274	−	26.3274i	−0.972424	−	0.972424i	0.0272063	−	0.999630i	$-0.491339\pi$
$733$	−26.3274	−	26.3274i	−0.972424	−	0.972424i	−0.999630	+	0.0272063i	$0.991339\pi$
$734$	−3.48622	−	13.0107i	−0.128679	−	0.480235i
$735$	8.54983	−	6.83352i	0.315365	−	0.252058i
$736$	2.49170	−	2.49170i	0.0918451	−	0.0918451i
$737$	−38.1242	−	22.0110i	−1.40432	−	0.810786i
$738$	3.15908	−	13.9812i	0.116287	−	0.514656i
$739$	−22.7470	−	6.09505i	−0.836763	−	0.224210i	−0.185101	−	0.982719i	$-0.559261\pi$
$739$	−22.7470	−	6.09505i	−0.836763	−	0.224210i	−0.651662	+	0.758509i	$0.725928\pi$
$740$	−11.3771			−0.418232
$741$	−7.57476	−	0.431130i	−0.278266	−	0.0158380i
$742$	4.04860			0.148629
$743$	40.3372	+	10.8083i	1.47983	+	0.396519i	0.906288	−	0.422660i	$-0.138903\pi$
$743$	40.3372	+	10.8083i	1.47983	+	0.396519i	0.573539	+	0.819178i	$0.305570\pi$
$744$	−0.00404361	+	0.00549141i	−0.000148246	+	0.000201325i
$745$	−4.00586	−	2.31278i	−0.146763	−	0.0847338i
$746$	24.0925	−	24.0925i	0.882089	−	0.882089i
$747$	−20.1376	−	10.5869i	−0.736795	−	0.387355i
$748$	2.94469	+	10.9897i	0.107669	+	0.401825i
$749$	0.456462	+	0.456462i	0.0166788	+	0.0166788i
$750$	−0.192053	+	1.72137i	−0.00701277	+	0.0628556i
$751$	−5.24153	+	3.02620i	−0.191266	+	0.110428i	−0.592575	−	0.805515i	$-0.701889\pi$
$751$	−5.24153	+	3.02620i	−0.191266	+	0.110428i	0.401309	+	0.915943i	$0.368555\pi$
$752$	2.56753	−	9.58216i	0.0936283	−	0.349425i
$753$	−46.7712	+	20.4668i	−1.70444	+	0.745850i
$754$	−22.6051	+	14.7409i	−0.823228	+	0.536831i
$755$		−	7.44661i		−	0.271010i
$756$	−3.55029	−	2.40358i	−0.129123	−	0.0874175i
$757$	−5.09098	−	8.81784i	−0.185035	−	0.320490i	0.758553	−	0.651611i	$-0.225906\pi$
$757$	−5.09098	−	8.81784i	−0.185035	−	0.320490i	−0.943588	+	0.331121i	$0.892573\pi$
$758$	11.9487	−	20.6958i	0.433997	−	0.751705i
$759$	21.5590	+	8.43418i	0.782542	+	0.306141i
$760$	1.17350	−	0.314438i	0.0425673	−	0.0114059i
$761$	−47.4705	+	12.7197i	−1.72080	+	0.461088i	−0.978031	−	0.208457i	$-0.933156\pi$
$761$	−47.4705	+	12.7197i	−1.72080	+	0.461088i	−0.742772	+	0.669545i	$0.766489\pi$
$762$	1.27360	+	0.498250i	0.0461377	+	0.0180497i
$763$	−0.293870	+	0.508999i	−0.0106388	+	0.0184270i
$764$	2.62831	+	4.55237i	0.0950889	+	0.164699i
$765$	−7.60903	+	4.80423i	−0.275105	+	0.173697i
$766$		−	22.6973i		−	0.820086i
$767$	14.6119	−	9.52851i	0.527606	−	0.344055i
$768$	1.58678	−	0.694363i	0.0572579	−	0.0250557i
$769$	−0.157880	+	0.589218i	−0.00569331	+	0.0212477i	−0.968714	−	0.248180i	$-0.920168\pi$
$769$	−0.157880	+	0.589218i	−0.00569331	+	0.0212477i	0.963021	+	0.269427i	$0.0868344\pi$
$770$	2.71034	−	1.56482i	0.0976740	−	0.0563921i
$771$	−2.48029	+	22.2309i	−0.0893255	+	0.800627i
$772$	−0.124615	−	0.124615i	−0.00448499	−	0.00448499i
$773$	−8.94546	−	33.3849i	−0.321746	−	1.20077i	−0.917543	−	0.397637i	$-0.869830\pi$
$773$	−8.94546	−	33.3849i	−0.321746	−	1.20077i	0.595797	−	0.803135i	$-0.296836\pi$
$774$	5.49201	−	10.4464i	0.197406	−	0.375489i
$775$	0.00278407	−	0.00278407i	0.000100007	−	0.000100007i
$776$	6.86499	+	3.96350i	0.246439	+	0.142281i
$777$	−9.64092	+	13.0928i	−0.345866	+	0.469703i
$778$	9.46711	+	2.53671i	0.339412	+	0.0909453i
$779$	5.80464			0.207973
$780$	6.23491	+	0.354870i	0.223245	+	0.0127064i
$781$	−22.3851			−0.801001
$782$	−10.2098	−	2.73570i	−0.365101	−	0.0978284i
$783$	−7.35536	−	38.1901i	−0.262859	−	1.36480i
$784$	5.47258	+	3.15960i	0.195449	+	0.112843i
$785$	−3.08843	+	3.08843i	−0.110231	+	0.110231i
$786$	0.832907	−	0.665707i	0.0297088	−	0.0237450i
$787$	−5.66965	−	21.1594i	−0.202101	−	0.754252i	−0.990314	−	0.138849i	$-0.955660\pi$
$787$	−5.66965	−	21.1594i	−0.202101	−	0.754252i	0.788212	−	0.615403i	$-0.211007\pi$
$788$	5.17241	+	5.17241i	0.184259	+	0.184259i
$789$	47.5046	+	5.30006i	1.69121	+	0.188687i
$790$	5.11782	−	2.95478i	0.182084	−	0.105126i
$791$	−1.33560	+	4.98453i	−0.0474885	+	0.177229i
$792$	8.35822	+	7.72146i	0.296996	+	0.274370i
$793$	−10.2153	+	48.5111i	−0.362757	+	1.72268i
$794$		−	25.0689i		−	0.889664i
$795$	−1.27582	−	8.40241i	−0.0452488	−	0.298003i
$796$	−9.76412	−	16.9120i	−0.346080	−	0.599428i
$797$	−5.47802	+	9.48820i	−0.194041	+	0.336089i	−0.946586	−	0.322452i	$-0.895493\pi$
$797$	−5.47802	+	9.48820i	−0.194041	+	0.336089i	0.752545	+	0.658541i	$0.228826\pi$
$798$	0.632560	−	1.61692i	0.0223924	−	0.0572382i
$799$	−28.7426	+	7.70155i	−1.01684	+	0.272461i
$800$	−0.965926	+	0.258819i	−0.0341506	+	0.00915064i
$801$	21.5248	−	0.852382i	0.760541	−	0.0301174i
$802$	−15.9007	+	27.5409i	−0.561474	+	0.972502i
$803$	−22.7718	−	39.4418i	−0.803598	−	1.39187i
$804$	19.8746	−	3.01777i	0.700925	−	0.106429i
$805$			2.90752i			0.102476i
$806$	−0.0105677	−	0.00947899i	−0.000372231	−	0.000333883i
$807$	−14.5234	−	33.1892i	−0.511247	−	1.16832i
$808$	3.98163	−	14.8596i	0.140073	−	0.522760i
$809$	7.08136	−	4.08842i	0.248967	−	0.143741i	−0.370324	−	0.928903i	$-0.620753\pi$
$809$	7.08136	−	4.08842i	0.248967	−	0.143741i	0.619291	+	0.785161i	$0.287420\pi$
$810$	−3.86957	+	8.12566i	−0.135963	+	0.285507i
$811$	−25.8013	−	25.8013i	−0.906006	−	0.906006i	0.0899413	−	0.995947i	$-0.471332\pi$
$811$	−25.8013	−	25.8013i	−0.906006	−	0.906006i	−0.995947	+	0.0899413i	$0.971332\pi$
$812$	−1.59840	−	5.96533i	−0.0560930	−	0.209342i
$813$	16.8732	+	21.1111i	0.591770	+	0.740399i
$814$	30.5140	−	30.5140i	1.06952	−	1.06952i
$815$	−4.41355	−	2.54816i	−0.154600	−	0.0892583i
$816$	−4.18360	−	3.08060i	−0.146455	−	0.107843i
$817$	4.61659	+	1.23701i	0.161514	+	0.0432776i
$818$	−22.4973			−0.786600
$819$	5.69181	−	6.87442i	0.198888	−	0.240212i
$820$	−4.77790			−0.166851
$821$	10.5495	+	2.82674i	0.368181	+	0.0986539i	0.438166	−	0.898894i	$-0.355628\pi$
$821$	10.5495	+	2.82674i	0.368181	+	0.0986539i	−0.0699844	+	0.997548i	$0.522295\pi$
$822$	14.9600	+	11.0158i	0.521791	+	0.384221i
$823$	41.3492	+	23.8730i	1.44134	+	0.832159i	0.997939	−	0.0641632i	$-0.0204378\pi$
$823$	41.3492	+	23.8730i	1.44134	+	0.832159i	0.443403	+	0.896322i	$0.353771\pi$
$824$	−11.5932	+	11.5932i	−0.403867	+	0.403867i
$825$	−4.10170	−	5.13189i	−0.142803	−	0.178670i
$826$	1.03321	+	3.85599i	0.0359499	+	0.134167i
$827$	−11.8144	−	11.8144i	−0.410828	−	0.410828i	0.471199	−	0.882027i	$-0.343821\pi$
$827$	−11.8144	−	11.8144i	−0.410828	−	0.410828i	−0.882027	+	0.471199i	$0.843821\pi$
$828$	−10.0949	+	3.13797i	−0.350822	+	0.109052i
$829$	−16.8509	+	9.72886i	−0.585255	+	0.337897i	−0.763219	−	0.646140i	$-0.776382\pi$
$829$	−16.8509	+	9.72886i	−0.585255	+	0.337897i	0.177964	+	0.984037i	$0.443049\pi$
$830$	−1.96279	+	7.32523i	−0.0681295	+	0.254263i
$831$	16.8795	+	38.5734i	0.585542	+	1.33810i
$832$	1.12067	+	3.42697i	0.0388523	+	0.118809i
$833$		−	18.9550i		−	0.656752i
$834$	39.6936	−	6.02709i	1.37448	−	0.208701i
$835$	4.60993	+	7.98464i	0.159533	+	0.276320i
$836$	−2.30404	+	3.99072i	−0.0796869	+	0.138022i
$837$	0.0184035	−	0.00893689i	0.000636118	−	0.000308904i
$838$	−18.1696	+	4.86852i	−0.627658	+	0.168180i
$839$	1.11041	−	0.297534i	0.0383357	−	0.0102720i	−0.239600	−	0.970872i	$-0.577016\pi$
$839$	1.11041	−	0.297534i	0.0383357	−	0.0102720i	0.277936	+	0.960600i	$0.410350\pi$
$840$	−0.520671	+	1.33091i	−0.0179649	+	0.0459208i
$841$	13.5109	−	23.4016i	0.465893	−	0.806950i
$842$	−16.2347	−	28.1193i	−0.559484	−	0.969055i
$843$	6.14611	+	40.4775i	0.211683	+	1.39412i
$844$		−	6.09178i		−	0.209688i
$845$	−1.98497	+	12.8476i	−0.0682852	+	0.441970i
$846$	−20.1947	+	21.8601i	−0.694309	+	0.751565i
$847$	−0.723258	+	2.69923i	−0.0248514	+	0.0927468i
$848$	4.24936	−	2.45337i	0.145924	−	0.0842490i
$849$	−38.8575	−	4.33531i	−1.33359	−	0.148788i
$850$	2.12103	+	2.12103i	0.0727508	+	0.0727508i
$851$	10.3762	+	38.7246i	0.355692	+	1.32746i
$852$	7.98496	−	6.38204i	0.273560	−	0.218645i
$853$	−35.2653	+	35.2653i	−1.20746	+	1.20746i	−0.235613	+	0.971847i	$0.575710\pi$
$853$	−35.2653	+	35.2653i	−1.20746	+	1.20746i	−0.971847	+	0.235613i	$0.924290\pi$
$854$	−9.82502	−	5.67248i	−0.336205	−	0.194108i
$855$	−3.55506	−	0.803273i	−0.121581	−	0.0274713i
$856$	0.755704	+	0.202490i	0.0258294	+	0.00692097i
$857$	−39.7560			−1.35804			−0.679020	−	0.734120i	$-0.737595\pi$
$857$	−39.7560			−1.35804			−0.679020	+	0.734120i	$0.737595\pi$
$858$	−17.6741	+	15.7705i	−0.603384	+	0.538397i
$859$	−38.7074			−1.32068			−0.660340	−	0.750967i	$-0.729588\pi$
$859$	−38.7074			−1.32068			−0.660340	+	0.750967i	$0.729588\pi$
$860$	−3.79999	−	1.01821i	−0.129579	−	0.0347205i
$861$	−4.04876	+	5.49841i	−0.137982	+	0.187385i
$862$	−18.9532	−	10.9426i	−0.645547	−	0.372707i
$863$	−2.57323	+	2.57323i	−0.0875939	+	0.0875939i	−0.749546	−	0.661952i	$-0.769728\pi$
$863$	−2.57323	+	2.57323i	−0.0875939	+	0.0875939i	0.661952	+	0.749546i	$0.269728\pi$
$864$	−5.18286	−	0.371368i	−0.176325	−	0.0126342i
$865$	−1.42312	−	5.31117i	−0.0483876	−	0.180585i
$866$	4.77724	+	4.77724i	0.162337	+	0.162337i
$867$	1.53689	−	13.7752i	0.0521956	−	0.467830i
$868$	0.00281344	−	0.00162434i	9.54945e−5	−	5.51337e-5i
$869$	−5.80139	+	21.6511i	−0.196799	+	0.734463i
$870$	−11.8767	+	5.19715i	−0.402656	+	0.176200i
$871$	2.26926	+	41.7850i	0.0768910	+	1.41583i
$872$			0.712318i			0.0241221i
$873$	−12.6961	−	20.1083i	−0.429698	−	0.680564i
$874$	−2.14052	−	3.70748i	−0.0724041	−	0.125408i
$875$	0.412555	−	0.714566i	0.0139469	−	0.0241568i
$876$	19.3679	+	7.57698i	0.654380	+	0.256003i
$877$	46.1278	−	12.3599i	1.55763	−	0.417365i	0.625715	−	0.780051i	$-0.284807\pi$
$877$	46.1278	−	12.3599i	1.55763	−	0.417365i	0.931911	+	0.362687i	$0.118141\pi$
$878$	26.2378	−	7.03041i	0.885484	−	0.237265i
$879$	−46.6631	−	18.2553i	−1.57391	−	0.615734i
$880$	1.89649	−	3.28482i	0.0639308	−	0.110731i
$881$	22.1331	+	38.3356i	0.745682	+	1.29156i	0.949875	+	0.312629i	$0.101210\pi$
$881$	22.1331	+	38.3356i	0.745682	+	1.29156i	−0.204193	+	0.978931i	$0.565457\pi$
$882$	−10.1210	−	16.0298i	−0.340792	−	0.539752i
$883$			30.2826i			1.01909i	0.860444	+	0.509545i	$0.170186\pi$
$883$			30.2826i			1.01909i	−0.860444	+	0.509545i	$0.829814\pi$
$884$	7.22153	−	8.05094i	0.242886	−	0.270783i
$885$	7.67708	−	3.35944i	0.258062	−	0.112926i
$886$	−7.90533	+	29.5031i	−0.265585	+	0.991176i
$887$	25.8425	−	14.9201i	0.867705	−	0.500970i	0.00111997	−	0.999999i	$-0.499644\pi$
$887$	25.8425	−	14.9201i	0.867705	−	0.500970i	0.866585	+	0.499030i	$0.166310\pi$
$888$	−2.18501	+	19.5843i	−0.0733241	+	0.657205i
$889$	−0.460674	−	0.460674i	−0.0154505	−	0.0154505i
$890$	−1.85846	−	6.93588i	−0.0622959	−	0.232491i
$891$	−11.4150	−	32.1718i	−0.382418	−	1.07780i
$892$	−5.87739	+	5.87739i	−0.196790	+	0.196790i
$893$	−10.4373	−	6.02599i	−0.349272	−	0.201652i
$894$	−4.75049	+	6.45139i	−0.158880	+	0.215767i
$895$	4.64624	+	1.24496i	0.155307	+	0.0416143i
$896$	−0.825110			−0.0275650
$897$	−4.47851	−	21.5455i	−0.149533	−	0.719384i
$898$	15.2586			0.509188
$899$	0.0284654	+	0.00762729i	0.000949375	+	0.000254384i
$900$	2.92623	+	0.661187i	0.0975411	+	0.0220396i
$901$	−12.7463	−	7.35910i	−0.424642	−	0.245167i
$902$	12.8146	−	12.8146i	0.426678	−	0.426678i
$903$	−4.39185	+	3.51022i	−0.146151	+	0.116813i
$904$	1.61869	+	6.04105i	0.0538369	+	0.200922i
$905$	6.84993	+	6.84993i	0.227699	+	0.227699i
$906$	−12.8184	−	1.43014i	−0.425862	−	0.0475132i
$907$	31.8087	−	18.3647i	1.05619	−	0.609791i	0.131814	−	0.991274i	$-0.457920\pi$
$907$	31.8087	−	18.3647i	1.05619	−	0.609791i	0.924376	+	0.381483i	$0.124587\pi$
$908$	−5.28248	+	19.7145i	−0.175305	+	0.654248i
$909$	−31.3172	+	33.8998i	−1.03873	+	1.12438i
$910$	−2.65328	−	1.34559i	−0.0879553	−	0.0446058i
$911$			35.9584i			1.19136i	0.803223	+	0.595678i	$0.203117\pi$
$911$			35.9584i			1.19136i	−0.803223	+	0.595678i	$0.796883\pi$
$912$	−0.315891	−	2.08041i	−0.0104602	−	0.0688894i
$913$	−14.3823	−	24.9109i	−0.475986	−	0.824431i
$914$	−1.83877	+	3.18485i	−0.0608212	+	0.105345i
$915$	−8.67645	+	22.1783i	−0.286835	+	0.733191i
$916$	−0.990963	+	0.265528i	−0.0327423	+	0.00877328i
$917$	−0.490632	+	0.131465i	−0.0162021	+	0.00434134i
$918$	6.80853	+	14.0206i	0.224715	+	0.462749i
$919$	−4.72834	+	8.18972i	−0.155974	+	0.270154i	−0.933413	−	0.358804i	$-0.883185\pi$
$919$	−4.72834	+	8.18972i	−0.155974	+	0.270154i	0.777440	+	0.628958i	$0.216518\pi$
$920$	1.76190	+	3.05169i	0.0580880	+	0.100611i
$921$	12.7821	−	1.94084i	0.421184	−	0.0639528i
$922$			19.1292i			0.629985i
$923$	11.6231	+	17.8240i	0.382579	+	0.586683i
$924$	−2.17310	−	4.96603i	−0.0714898	−	0.163370i
$925$	2.94462	−	10.9895i	0.0968185	−	0.361332i
$926$	−34.4914	+	19.9136i	−1.13346	+	0.654401i
$927$	46.9687	−	14.6001i	1.54265	−	0.479530i
$928$	−5.29253	−	5.29253i	−0.173736	−	0.173736i
$929$	−6.29712	−	23.5012i	−0.206602	−	0.771048i	−0.988955	−	0.148214i	$-0.952648\pi$
$929$	−6.29712	−	23.5012i	−0.206602	−	0.771048i	0.782354	−	0.622834i	$-0.214019\pi$
$930$	−0.00425773	−	0.00532711i	−0.000139616	−	0.000174683i
$931$	5.42857	−	5.42857i	0.177914	−	0.177914i
$932$	−10.1167	−	5.84090i	−0.331385	−	0.191325i
$933$	−24.1170	−	17.7586i	−0.789555	−	0.581390i
$934$	−30.6054	−	8.20070i	−1.00144	−	0.268335i
$935$	−11.3774			−0.372081
$936$	1.80829	−	10.6644i	0.0591059	−	0.348578i
$937$	−33.2229			−1.08534			−0.542672	−	0.839945i	$-0.682587\pi$
$937$	−33.2229			−1.08534			−0.542672	+	0.839945i	$0.682587\pi$
$938$	−9.25005	−	2.47854i	−0.302025	−	0.0809273i
$939$	5.18033	+	3.81454i	0.169054	+	0.124483i
$940$	8.59113	+	4.96009i	0.280212	+	0.161780i
$941$	−5.22787	+	5.22787i	−0.170424	+	0.170424i	−0.787166	−	0.616742i	$-0.788452\pi$
$941$	−5.22787	+	5.22787i	−0.170424	+	0.170424i	0.616742	+	0.787166i	$0.288452\pi$
$942$	4.72319	+	5.90947i	0.153890	+	0.192541i
$943$	4.35756	+	16.2626i	0.141902	+	0.529584i
$944$	3.42109	+	3.42109i	0.111347	+	0.111347i
$945$	3.24057	−	2.80722i	0.105416	−	0.0913190i
$946$	12.9226	−	7.46089i	0.420151	−	0.242574i
$947$	4.28531	−	15.9930i	0.139254	−	0.519703i	−0.860690	−	0.509129i	$-0.829968\pi$
$947$	4.28531	−	15.9930i	0.139254	−	0.519703i	0.999944	−	0.0105737i	$-0.00336579\pi$
$948$	−4.10337	−	9.37714i	−0.133271	−	0.304555i
$949$	−19.5814	+	38.6114i	−0.635640	+	1.25338i
$950$			1.21489i			0.0394164i
$951$	28.7749	−	4.36920i	0.933091	−	0.141681i
$952$	1.23750	+	2.14341i	0.0401075	+	0.0694682i
$953$	−3.83233	+	6.63779i	−0.124141	+	0.215019i	−0.921397	−	0.388623i	$-0.872951\pi$
$953$	−3.83233	+	6.63779i	−0.124141	+	0.215019i	0.797256	+	0.603642i	$0.206284\pi$
$954$	−14.7087	+	0.582463i	−0.476211	+	0.0188580i
$955$	−5.07751	+	1.36051i	−0.164304	+	0.0440252i
$956$	−19.6542	+	5.26633i	−0.635662	+	0.170325i
$957$	17.9148	−	45.7928i	0.579102	−	1.48027i
$958$	−12.8383	+	22.2366i	−0.414788	+	0.718433i
$959$	−4.42513	−	7.66455i	−0.142895	−	0.247501i
$960$	0.260015	+	1.71242i	0.00839195	+	0.0552682i
$961$		−	31.0000i		−	0.999999i
$962$	−40.1405	−	8.45267i	−1.29418	−	0.272525i
$963$	−1.72401	−	1.59267i	−0.0555555	−	0.0513231i
$964$	4.66870	−	17.4238i	0.150369	−	0.561184i
$965$	0.152621	−	0.0881160i	0.00491306	−	0.00283655i
$966$	5.00491	+	0.558396i	0.161030	+	0.0179661i
$967$	−19.4699	−	19.4699i	−0.626110	−	0.626110i	0.320977	−	0.947087i	$-0.395989\pi$
$967$	−19.4699	−	19.4699i	−0.626110	−	0.626110i	−0.947087	+	0.320977i	$0.895989\pi$
$968$	0.876559	+	3.27136i	0.0281737	+	0.105146i
$969$	−4.93056	+	3.94079i	−0.158393	+	0.126596i
$970$	−5.60524	+	5.60524i	−0.179973	+	0.179973i
$971$	−43.2649	−	24.9790i	−1.38844	−	0.801613i	−0.395296	−	0.918554i	$-0.629358\pi$
$971$	−43.2649	−	24.9790i	−1.38844	−	0.801613i	−0.993139	+	0.116940i	$0.962691\pi$
$972$	13.2441	+	8.22152i	0.424805	+	0.263705i
$973$	−18.4742	−	4.95014i	−0.592255	−	0.158694i
$974$	24.0727			0.771340
$975$	−1.95649	+	5.93061i	−0.0626579	+	0.189932i
$976$	−13.7496			−0.440115
$977$	−27.6307	−	7.40363i	−0.883985	−	0.236863i	−0.211859	−	0.977300i	$-0.567952\pi$
$977$	−27.6307	−	7.40363i	−0.883985	−	0.236863i	−0.672126	+	0.740437i	$0.734618\pi$
$978$	−5.23397	+	7.10797i	−0.167364	+	0.227288i
$979$	23.5869	+	13.6179i	0.753839	+	0.435229i
$980$	−4.46834	+	4.46834i	−0.142736	+	0.142736i
$981$	0.994412	−	1.89149i	0.0317491	−	0.0603905i
$982$	−2.59493	−	9.68440i	−0.0828074	−	0.309042i
$983$	31.5486	+	31.5486i	1.00624	+	1.00624i	0.999980	+	0.00626241i	$0.00199340\pi$
$983$	31.5486	+	31.5486i	1.00624	+	1.00624i	0.00626241	+	0.999980i	$0.498007\pi$
$984$	−0.917607	+	8.22453i	−0.0292523	+	0.262189i
$985$	−6.33488	+	3.65744i	−0.201846	+	0.116536i
$986$	−5.81081	+	21.6862i	−0.185054	+	0.690631i
$987$	12.9882	−	5.68353i	0.413418	−	0.180909i
$988$	4.37392	−	0.237539i	0.139153	−	0.00755712i
$989$			13.8627i			0.440810i
$990$	−9.62163	+	6.07496i	−0.305795	+	0.193075i
$991$	16.8825	+	29.2414i	0.536291	+	0.928883i	0.999100	+	0.0424251i	$0.0135084\pi$
$991$	16.8825	+	29.2414i	0.536291	+	0.928883i	−0.462809	+	0.886458i	$0.653158\pi$
$992$	0.00196864	−	0.00340978i	6.25043e−5	−	0.000108261i
$993$	31.3704	+	12.2726i	0.995511	+	0.389458i
$994$	−4.70362	+	1.26033i	−0.149190	+	0.0399753i
$995$	18.8628	−	5.05428i	0.597992	−	0.160231i
$996$	12.2325	+	4.78552i	0.387601	+	0.151635i
$997$	−3.58159	+	6.20350i	−0.113430	+	0.196467i	−0.917151	−	0.398540i	$-0.869517\pi$
$997$	−3.58159	+	6.20350i	−0.113430	+	0.196467i	0.803721	+	0.595006i	$0.202850\pi$
$998$	10.7600	+	18.6369i	0.340603	+	0.589942i
$999$	33.1421	−	48.9537i	1.04857	−	1.54883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bh.c.11.2	✓	40
3.2	odd	2	inner	390.2.bh.c.11.7	yes	40
13.6	odd	12	inner	390.2.bh.c.71.7	yes	40
39.32	even	12	inner	390.2.bh.c.71.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bh.c.11.2	✓	40	1.1	even	1	trivial
390.2.bh.c.11.7	yes	40	3.2	odd	2	inner
390.2.bh.c.71.2	yes	40	39.32	even	12	inner
390.2.bh.c.71.7	yes	40	13.6	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.39472 - 1.02701i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.08139 + 1.35299i) q^{6} +(-0.213554 - 0.796995i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.890511 + 2.86478i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-1.39472 - 1.02701i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.08139 + 1.35299i) q^{6} +(-0.213554 - 0.796995i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.890511 + 2.86478i) q^{9} +(0.866025 - 0.500000i) q^{10} +(-0.981698 + 3.66375i) q^{11} +(-0.694363 - 1.58678i) q^{12} +(3.42697 - 1.12067i) q^{13} +0.825110i q^{14} +(1.71242 - 0.260015i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.49980 - 2.59772i) q^{17} +(-0.118707 - 2.99765i) q^{18} +(1.17350 - 0.314438i) q^{19} +(-0.965926 + 0.258819i) q^{20} +(-0.520671 + 1.33091i) q^{21} +(1.89649 - 3.28482i) q^{22} +(1.76190 + 3.05169i) q^{23} +(0.260015 + 1.71242i) q^{24} -1.00000i q^{25} +(-3.60025 + 0.195522i) q^{26} +(1.70014 - 4.91015i) q^{27} +(0.213554 - 0.796995i) q^{28} +(6.48200 - 3.74239i) q^{29} +(-1.72137 - 0.192053i) q^{30} +(0.00278407 + 0.00278407i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(5.13189 - 4.10170i) q^{33} +(-2.12103 + 2.12103i) q^{34} +(0.714566 + 0.412555i) q^{35} +(-0.661187 + 2.92623i) q^{36} +(10.9895 + 2.94462i) q^{37} -1.21489 q^{38} +(-5.93061 - 1.95649i) q^{39} +1.00000 q^{40} +(4.61510 + 1.23661i) q^{41} +(0.847394 - 1.15080i) q^{42} +(3.40698 + 1.96702i) q^{43} +(-2.68205 + 2.68205i) q^{44} +(-2.65539 - 1.39602i) q^{45} +(-0.912024 - 3.40372i) q^{46} +(-7.01463 - 7.01463i) q^{47} +(0.192053 - 1.72137i) q^{48} +(5.47258 - 3.15960i) q^{49} +(-0.258819 + 0.965926i) q^{50} +(-4.75968 + 2.08280i) q^{51} +(3.52818 + 0.742952i) q^{52} -4.90674i q^{53} +(-2.91305 + 4.30281i) q^{54} +(-1.89649 - 3.28482i) q^{55} +(-0.412555 + 0.714566i) q^{56} +(-1.95964 - 0.766637i) q^{57} +(-7.22973 + 1.93720i) q^{58} +(4.67330 - 1.25221i) q^{59} +(1.61301 + 0.631032i) q^{60} +(-6.87481 + 11.9075i) q^{61} +(-0.00196864 - 0.00340978i) q^{62} +(2.09305 - 1.32152i) q^{63} +1.00000i q^{64} +(-1.63080 + 3.21567i) q^{65} +(-6.01863 + 2.63371i) q^{66} +(-3.00389 + 11.2107i) q^{67} +(2.59772 - 1.49980i) q^{68} +(0.676753 - 6.06575i) q^{69} +(-0.583441 - 0.583441i) q^{70} +(1.52747 + 5.70060i) q^{71} +(1.39602 - 2.65539i) q^{72} +(-8.49044 + 8.49044i) q^{73} +(-9.85289 - 5.68857i) q^{74} +(-1.02701 + 1.39472i) q^{75} +(1.17350 + 0.314438i) q^{76} +3.12963 q^{77} +(5.22215 + 3.42478i) q^{78} +5.90955 q^{79} +(-0.965926 - 0.258819i) q^{80} +(-7.41398 + 5.10224i) q^{81} +(-4.13778 - 2.38895i) q^{82} +(-5.36244 + 5.36244i) q^{83} +(-1.11637 + 0.892267i) q^{84} +(0.776351 + 2.89738i) q^{85} +(-2.78179 - 2.78179i) q^{86} +(-12.8841 - 1.43747i) q^{87} +(3.28482 - 1.89649i) q^{88} +(1.85846 - 6.93588i) q^{89} +(2.20360 + 2.03572i) q^{90} +(-1.62501 - 2.49195i) q^{91} +3.52379i q^{92} +(-0.00102375 - 0.00674227i) q^{93} +(4.96009 + 8.59113i) q^{94} +(-0.607447 + 1.05213i) q^{95} +(-0.631032 + 1.61301i) q^{96} +(-7.65690 + 2.05166i) q^{97} +(-6.10387 + 1.63553i) q^{98} +(-11.3701 + 0.450254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9	\( 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9} + 8 q^{13} + 4 q^{15} + 20 q^{16} - 8 q^{18} - 16 q^{19} + 4 q^{21} - 8 q^{22} + 8 q^{24} - 48 q^{27} + 8 q^{28} + 36 q^{31} + 12 q^{33} + 16 q^{34} - 12 q^{36} - 64 q^{37} - 60 q^{39} + 40 q^{40} - 12 q^{42} + 8 q^{45} - 32 q^{46} + 48 q^{49} + 24 q^{52} - 28 q^{54} + 8 q^{55} - 76 q^{57} - 28 q^{58} + 4 q^{60} - 40 q^{61} + 80 q^{63} + 40 q^{66} - 28 q^{67} - 36 q^{69} + 16 q^{70} + 16 q^{72} + 8 q^{73} - 16 q^{76} - 28 q^{78} + 40 q^{79} + 12 q^{81} + 20 q^{84} + 44 q^{85} + 40 q^{87} + 12 q^{88} + 120 q^{91} - 8 q^{93} - 16 q^{94} + 4 q^{96} - 160 q^{97} - 96 q^{99}+O(q^{100}) \) 40 * q + 8 * q^6 - 8 * q^7 + 8 * q^9 + 8 * q^13 + 4 * q^15 + 20 * q^16 - 8 * q^18 - 16 * q^19 + 4 * q^21 - 8 * q^22 + 8 * q^24 - 48 * q^27 + 8 * q^28 + 36 * q^31 + 12 * q^33 + 16 * q^34 - 12 * q^36 - 64 * q^37 - 60 * q^39 + 40 * q^40 - 12 * q^42 + 8 * q^45 - 32 * q^46 + 48 * q^49 + 24 * q^52 - 28 * q^54 + 8 * q^55 - 76 * q^57 - 28 * q^58 + 4 * q^60 - 40 * q^61 + 80 * q^63 + 40 * q^66 - 28 * q^67 - 36 * q^69 + 16 * q^70 + 16 * q^72 + 8 * q^73 - 16 * q^76 - 28 * q^78 + 40 * q^79 + 12 * q^81 + 20 * q^84 + 44 * q^85 + 40 * q^87 + 12 * q^88 + 120 * q^91 - 8 * q^93 - 16 * q^94 + 4 * q^96 - 160 * q^97 - 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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